Missy's Gadget from Death In Heaven
by Stuart Galloway

Download: https://www.thingiverse.com/thing:1003036

Romana's Sonic Screwdriver from The Horns of Nimon
by Stuart Galloway

Download: https://www.thingiverse.com/thing:979881

Metebelis III Crystal from The Green Death and Planet of Spiders
by Stuart Galloway

Download: https://www.thingiverse.com/thing:857681

Rose Tyler Dalek Blaster from The Stolen Earth
by AprilStorm

Download: https://www.thingiverse.com/thing:240398

Full Sized New-Series Dalek
by Matt Palulis (and others)

Download: https://www.thingiverse.com/thing:2576488

Notes: While this is jaw-dropping gorgeous, please note that Matt printed these things on two different custom-built printers, with significantly larger build areas than most people have at home. However, if you're building a Dalek and looking for specific parts to complete your design, this is a good place to pick up bits that you don't feel like fabricating or buying online.

6th Doctor's Sonic Lance from Attack of the Cybermen
by Various

Edward Baum LED version: https://www.thingiverse.com/thing:3446209
David Dunlap version: https://www.thingiverse.com/thing:4493652
Stephen Miller version: https://www.thingiverse.com/thing:2454850

Notes: Several individuals have taken a stab at recreating this prop, but nobody seems to have gotten the proportions exactly right yet. (To be fair, there aren't many good source images.) Edward Baum's version is a hollow clamshell design with a functional button for triggering an internal LED, though I think David Dunlap's version is slightly closer to replicating the overall shape correctly, though none of them include the thumb slider on the right-hand side.

Romana I's Dress Clasp from The Ribos Operation
by Edward Baum

Download: https://www.thingiverse.com/thing:2899190

Gallifreyan Staser Rifle from Day of the Doctor/Hell Bent
by Ron Goldberg

Download: (Files have been removed)

Notes: This turns into an absolutely gorgeous prop when professionally sanded, assembled, and painted. (Image below courtesy of Agents of Chaos design) Sadly, it appears the designer has deleted his thingiverse account, so unless I can get his permission to repost the files elsewhere, this design is currently unavailable.

Cyberman Gun from Earthshock/The Five Doctors/Attack of the Cybermen
by Ron Goldberg

Download: (Files have been removed)

Notes: Another gorgeous prop, but like the Staser Rifle, the designer has deleted his thingiverse account, so unless I can get his permission to repost the files elsewhere, this design is currently unavailable.

Alien Coins from Planet of Fire
by Wim Ruijter

Download: https://drive.google.com/drive/folders/1Ao-qcWW0OTbO6BVx99WSpjrySdUfs0PL

Gallifreyan Staser Pistol from Day of the Doctor/Hell Bent
by David Dunlap

Download: https://www.thingiverse.com/thing:4203690

Notes: This prop is designed to be printed in two halves directly on your build plate (or borosilicate glass plate), no raft necessary.

Dalek Projenitor from Victory of the Daleks
by Stephen Miller

Download: https://www.thingiverse.com/thing:3202041

Notes: This prop is a single solid piece, ideal for resin printers. If you are filament printing, you may want to consider splitting it into two halves and printing it directly on your build plate (or borosilicate glass plate) without a raft to minimize overhangs.

Home Box from Time of the Angels
by Stephen Miller

Download: https://www.thingiverse.com/thing:2926562

Notes: This prop is a single solid piece, but because it's quite large and contains two concave depressions, you will probably want to split it into chunks so that all depressions are printed facing upwards and there are no overhangs.
Personally, I would slice the cube into four separate pieces: The side that has River's writing (about midway between the edge and the rim of the circle), the same on the opposite side that doesn't have writing, then the rest of the box split lengthwise the other direction through the center of the ridged part in the middle. This will make sure that all major surface detail is printed facing upwards for maximum quality.

Siege Mode TARDIS from Flatline
by Stephen Miller

Download: https://www.thingiverse.com/thing:2400518

Notes: All six sides are pre-cut to be printed separately. This may even be small enough to fit on resin printers.

Full-Sized K-9
by Ian Hughes

Download: https://onedrive.live.com/?cid=bb21259d5a1270f4&id=BB21259D5A1270F4%21245158&authkey=!AAF7fDRdRBs8g0w
Or files can also be found in the files section of the K-9 Builder's Group: https://www.facebook.com/groups/196432204531886/permalink/799219040919863

Notes: This is probably one of the most epic 3D printer builds ever, and unlike the 3D printed full-scale Dalek above, Ian's version should be fully printable from a regular sized home 3D printer. It'll just take a really long time and a ton of filament. On the plus side, when you're finally done printing several months from now, you'll have a gorgeous full-scale Timelord's best friend, who's incredibly light weight, durable, and includes all the mounts you need to add motors to make him fully remote controlled!
As this is a build not to be undertaken lightly, I highly recommend checking out the K-9 Builder's Group on Facebook first, to get a better undetstanding of what other builders have done before you, and how massive a dent it'll put in your wallet.

First Doctor's Sonic from Lego Dimensions
by CaptainJimiPie

Download: https://www.thingiverse.com/thing:4755395

Notes: Based off the version from the Lego Dimensions video game.

Full-Sized Cybermen Helmets
from The Tenth Planet, Wheel in Space, The Invasion, and Earthshock
by Paul Lawrence-Jennings

Download:

The Tenth Planet Cyberman: https://www.thingiverse.com/thing:4726600
Wheel In Space Cyberman: https://www.thingiverse.com/thing:4726613
The Invasion Cyberman: https://www.thingiverse.com/thing:4726621
Earthshock Cyberman: https://www.thingiverse.com/thing:4726469

Notes: These helmets have been parted out into smaller pieces to fit on more modern-sized 3D printers.

The Master's TCE from Spyfall
by Rob Ackers

Download: https://drive.google.com/file/d/10qTRwvidVCk0gJr2VfaVCUxXtfNppaPU

Notes: The updated Tissue Compression Eliminator used by the Sacha Dhawan version of The Master from Spyfall.

War Master's Laser Screwdriver from Rage of the Timelords
by Rob Ackers

Download: https://drive.google.com/file/d/1Ju52C2tZH9jCItSrwovw80KGRrbCGrur

Notes: The War Master's Laser Screwdriver as seen on the cover of the Big Finish audio drama Rage of the Timelords.

The Rani and Tetrap Bracelet from Mark of the Rani and Time and the Rani
by Jason McLachlan

Download: https://www.thingiverse.com/thing:4632692

Notes: This is a bit of a cheat since it's technically a Blake's 7 prop... but one that got reused at least twice on Doctor Who by The Rani and her Tetrap minions. The Doctor Who version has a slightly different button face stuck over the top of the preexisting control panel, but it should be rather easy to alter.

If you're a Blake's 7 fan, he's got the Liberator Teleport Bracelets too, as well as an incredible assortment of Star Wars and Comic Book related costume props.

Cybermat from Wheel In Space
by Stephen Roberts

Download: https://www.thingiverse.com/thing:2938647

Notes: This template isn't fully screen accurate, but is designed for remote control and light support.

The Master's TCE from Colony in Space and Claws of Axos
by Rob Ackers

Download: https://drive.google.com/file/d/18CaZQEbTW_xF7NN4kI5hw0b_qnnZ9n58

Notes: The version of the Tissue Compression Eliminator used by Roger Delgado in Season 9.

Neural Relay from Hell Bent
by Rob Ackers

Download: https://drive.google.com/file/d/1SQbAB_Pn9cKFQJGIER7bfdkwjgnlfB6P

Notes: The mind-wiping neural relay device used by The Doctor and Clara in Hell Bent.

Adipose Pill Pendant from Partners in Crime
by Rob Ackers

Download: https://drive.google.com/file/d/1GF_hC2W3Te14kjZjzfoC8A6QFTnW0B_S

Notes: Not to be taken internally.

Sonic Screwdriver from Dark Eyes and Doom Coalition
by Rob Ackers

Download: https://drive.google.com/file/d/1GLQbp5rfc9jeI6ZCWu3qRH3oEmuA7VzM

Notes: The sonic screwdriver used in the Big Finish audio series Dark Eyes and Doom Coalition.

7th Doctor Signal Detector from Ghostlight and Dimensions in Time
by Rob Ackers

Download: https://drive.google.com/file/d/1OiJpybUwzpEjEvKPnt-Vhb2UZC-I7MaU

Notes: Requires a telescoping magnetic pickup as the antenna.

Movellan Virus Capsules from Ressurection of the Daleks
by Rob Ackers

Download: https://drive.google.com/file/d/1bCPIEJlfSa9Fa-opJuuMP3KcCyisjosm

Notes: Comes in both clean and damaged variants.

TARDIS Tool Kit from Earthshock
by Rob Ackers

Download: https://drive.google.com/file/d/1UzRdS-04OmQfY21y4YUiWcYdJsJgmFSa

Notes: Currently untested.

7th Doctor's Spoons from Time and the Rani
by Rob Ackers

Download: https://drive.google.com/file/d/1EcCVeHuh2hb940-NoPD_MUV5UjLQ93Po

Notes: This must be printed flat on a filament printer so the plastic can be heat formed to make the spoon shape.

Division Badge from Survivors of the Flux/The Vanquishers
by Rob Ackers

Download: https://drive.google.com/file/d/1biuy9_dIKrflHrcCr3jVlWqLCg-ONKfQ

13th Doctor Fob Watch from Survivors of the Flux/The Vanquishers
by Rob Ackers

Download: https://drive.google.com/file/d/1jJRtTmNOSi9TCfpdVmsRxIkOuIGBOVy_

Key to Time from The Armageddon Factor
by Dan Liwszyc

Download: https://drive.google.com/file/d/1t5vehJbnApIBe0e96cKDvVaDj5x1jyAI/

Notes: This is the full-scale 1:1 prop, designed to be printed out of transparent resin. However, the pieces will not fit on a standard sized resin printer, and the largest pieces (segments 1 and 5) just barely fits on the build plate of the Phrozen Transform, which is currently the largest home use resin printer on the market.
Assuming you already had a $3000 printer large enough to handle the print job, this would be incredibly costly to print solid, assuming the suction force didn't rip it off the build plate after the first couple of layers. If you want to reproduce the Key to Time prop, your best bet would be to try to print the pieces out of regular PLA filament so you get the basic shapes, sand then down nice and smooth to remove the layer lines, then take inverse plaster or silicon molds of the pieces and fill those molds with off-the-shelf clear epoxy resin. It will take some skill to do this without a single air bubble, but it would be cheaper and better looking in the long run. Plus you then have the molds handy to make more or pass them on to somebody else.

Alpha Centauri Coin from Greatest Show in the Galaxy
by Leighton Humphrey

Download: https://drive.google.com/file/d/1vDdeFSxGEdCSFtp9iw1TPr1LVdiMNT3O/

Notes: Can be printed double-sided (for SLA resin) or as separate pieces and sandwiched together (recommended for PLA).

Kane's Soverign from Dragonfire
by Leighton Humphrey

Download: https://drive.google.com/file/d/1g0n1HFQzrnbWV6sd7grFN8aulEZVSMGJ/

Notes: Comes in both a battered (more screen accurate) and clean version.

15th Doctor's Sonic from various
by Rob Ackers

Download: https://drive.google.com/file/d/1ipfGC3xgVRSD4uiBoOhagPwTLGR12aHC/

Notes: Still a work in progress.

2nd Doctor Sonics from various
by CaptainJimiPie

Download: https://www.thingiverse.com/thing:4815199/

Notes: Three different designs from Fury from the Deep, The Dominators, and The War Games.
The two pen light designs are made to fit a rechargeable USB penlight available here or here.

Clockwork Droid mask from The Girl in the Fireplace
by Leighton Humphrey

Download: https://drive.google.com/file/d/1Qw9vMh3g1O2ayRI_iZAEe5Hj-a2kmYB8/

Notes: Comes in a high quality version for resin printing and low poly for standard FDM printing.

70's/80's TARDIS Key from Various
by Troy Ryan Wood

Download: https://drive.google.com/file/d/1qgRDXrO2iX0JdBf6B4vvPGoxchHAAs5w

Notes: Comes in three variants: SLA (which has both sides rendered in higher detail for resin printing) a PLA-Flat version (no star map on bottom, designed to be printed flat on the build plate) and a PLA-Split version (with top and bottom as separate pieces that will need to be printed flat and glued together.)

Note that because this was designed to mimic the metal version of the key, the key ring hole at the top is fairly thin, and may break if twisted too hard. If printing out of SLA, I highly recommend using some flexibile resin like 3DMaterials SuperFlex or SirayaTech Tenacious as a strengthening agent (usually 20 to 25% by volume is sufficient.)