Android: One of Android's biggest weaknesses, at least compared to the iPhone, is its on-screen keyboard. ThickButtons tries to improve Android's typing experience by guessing what words you might be typing and enlarging the next letter you'll type, and it (mostly) succeeds.
Designer Lukas Mathias has thoroughly detailed the differences in iPhone and Android one-finger typing. The major improvement on the Apple side of the scale is that the iPhone quietly and invisibly enlarges the "hit area" for the letters you're most likely to type next, based on your own word use and the built-in dictionary. ThickButtons seems inspired by the lack of such a feature on the Android keyboard's uniformly sized buttons.
As you start typing, ThickButtons' keyboard replacement looks at the words that the Android system normally suggests for auto-completion, then enlarges and lightly colour-shades the keys that correspond to the next letters in each of those words. If there are a lot of words that have a letter that follows what you just typed, that letter gets super-sized. Type "t-h," for example, and "e" will balloon up as a likely candidate, and it's easier to hit with your thumb.
I've only had about 30 minutes to test out ThickButtons, but, on the whole, I like how it works. I often forget that auto-complete suggestions are right above the keyboard, and sometimes find them more effort than they're worth to reach up and hit, so getting a halfway solution of auto-enlarging keys is right up my alley. Then again, when I'm typing out a word that Android would not have guessed I was going for, seeing the other letters all lit up and enlarged can cause a slight distraction as I try to peck out my word. When ThickButtons is right about what you're writing, it's really helpful; when it's wrong, it can be a slight inconvenience for some. That's a worthy trade, I'd think.
You can customise which dictionaries (default, contacts, SMS) ThickButtons pulls from in your Locale & Keyboard settings, and you'll want to read ThickButtons' installation instructions for enabling it on your system. It's a free download, at least while it's in its beta phase, and found in the Market and at the developers' site.