Tools

From Dr. Mario
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See also Rom Hacks.

NES

Bo Krif Ulse
A maneuver trainer. It is a Lua script for fceux. It lets you play a custom scenario: you can choose what the game board looks like (where all the viruses pill halves are) and what pill to control, and practice placing that pill on that board over and over. It comes with some example maneuvers to practice and instructions on creating your own. See the creator testing it and dmhero using it to set up a 6x6 single-color clear for examples.
Dr. Mario ngrams
This is an exact implementation of the NES' pill generation RNG, plus a thin wrapper on top to generate some statistics and visualizations of the sequences. It can be used to generate diagrams showing how likely 1-, 2-, or 3-long pill sequences are compared to how likely they should be if the RNG were truly uniformly random. The linked directory also contains the diagrams and sequences produced by the program, so that non-experts can simply peruse the visualizations or do their own analyses.
a web clone
A javascript reimplementation. It sports faithful level and pill generation and movement mechanics, but is still a work-in-progress. Use WASD for directions, JK for rotations.
an AI
This is a Dr. Mario AI. It cheats a little bit: it doesn't actually move the pills, just magically modifies memory for them to be in the right place. But working out where to put the pills is the hard part anyway; actually working out how to get them there is fairly straightforward, so it's addressed the interesting part.

Other

Recommended timers
LiveSplit
WSplit
urn if you need native Linux support
wiimmfi
A way to play Dr. Mario Online RX (the Wii release) with other people over the Internet. You must patch your copy of the game following the instructions at that site. It can also be made to work with dolphin.
SNES preseed
This is a ROM patcher for the SNES version of the game. It lets you pick a specific seed, and modify a ROM to always start from that seed. For example, if you wanted to race somebody else, and be sure you both got the same virus layout and pill sequence, you could pick a random number and use this to get a fair comparison.