News and Weather (Pre-installed): Whenever i have a few spare minutes i'll often pop this open to see if there's any new articles available. And the past couple weeks i've also been checking it to see when the rain is supposed to be starting or stopping. The initial selection of news was pretty poor. There was a lot of celebrity and entertainment crap, so i got rid of all the regular topic except for "Sci/Tech." Luckily you can create your own topics, which are presumably just fed through Google News. Within the first week i'd added "Video Games," "1UP," "Android," "Kotaku," "Nintendo," and "Enix." Perhaps i ought to take some time and figure out some more topics to add, but this set seems to be serving pretty well so far.
Browser (Pre-installed): Duh. I've got those pages of favorite links i put together, plus the bookmarks i've made in the browser itself. The most common use of it has got to be looking up the answers to random questions in Wikipedia :) Also, since we don't currently have the living room in a configuration were i can move the monitor and keyboard over to the table it makes an easy alternative for reading FAQs. For Valkyria Chronicles i've been tossing all the most frequently references tables and such into a single Google Doc so i can see it all on one page.
Maps (Pre-installed): This is about half used for getting directions to places, and half for looking up places. Frequently restaurants.
Gmail (Pre-installed): I don't use it to compose mail usually, but i'll often take a quick look to see what's up whenever it alerts me incoming mail.
List Master (Free/$1.50): Great for keeping track of just about anything that can be put into a list format. I've currently got over 20 lists with... looks like about 99 items spread between them. I probably ought to do a little housekeeping on those lists though. On ones where i actually do check things off i'm bad about going through and deleting the checked off items later.
Foursquare (Free): I picked this up to to play around with because of the PvP comics about it/Gowalla. It's like posting your location on Buzz, except it's not actually linked to your gmail account (which is a plus in my mind) and there are achievements to unlock. Since i don't have a lot of friends that i hang out with nearby i'm not sure posting the information provides any practical benefit, and i may get bored with it once i've gotten all the easy achievements.
The Weather Channel (Free): When the very rough forecasts given by the News and Weather app aren't good enough this is what i load up.
Volume Control (Free): Simple little app that lets you set the volume level you want. It will run in the background and reset the volume if you ever accidentally change it. I don't exactly _use_ it a lot, but i've always got it running.
OpenSudoku (Free): I'm not very good at Sudoku, but it does provide a simple and easy distraction that i an pick up when i've got a little time to kill (and have run out of news articles to read) and can put down as soon as something else needs my attention without losing my place.
YouTube (Pre-installed): I don't usually look for or get sent links to YouTube vids when i'm not at the PC. However there have been occasions where i've been someplace random with shelleycat and said "what! You've never seen that video?!" and pulled it out to show her. Like with Jonathan Coulton's "Ikea" song right before the concert :)
Talk (Pre-installed): I pretty much only use this to chat with shelleycat when i'm not at a computer.
Nesoid and SNesoid ($3.50 and $4): NES and SNES emulators. I tried out the demo versions just long enough to verify that they worked and then bought the full versions right away. Unfortunately(?) i don't have large amounts of time where i want to play a game but aren't near my PC or consoles. Plus i'd be worried about draining the battery life. However if it's ever necessary i have access to most of the Final Fantasy and Dragon Quest games, Nobunaga's Ambition and most of the Romance of the Three Kingdoms games, Gemfire, Bahamut Lagoon, and a random selection of other games available.
CardioTrainer (Free): Used to keep track of your exercise. I haven't used it much yet, but i'm hoping i will be once it's warm enough outside to go rollerblading again.
Listen (Free): Google app for listening to podcasts. I probably _would_ use this to listen to 1UP and GameSpot, but i usually take notes on podcasts when i'm listening to them. Not extensive notes, just enough so that if i ever want to find "that podcast where they talked about that one cool thing" i have at least a hope of doing so. That means that i have to be at a computer when i'm listening to them, so there's no point and listening to them via my phone.
FeedR Demo (Free): An RSS Feed reader. I've never gotten very much into the whole RSS feed. I decided to try this out because the demo was free (not sure how much the "Pro" or whatever version is) however i have no idea what feeds to add to it. I found a couple 1UP and GameSpot feeds, but i never remember to check it anyways. I suppose if i actually had a lot of feeds to keep track of i'd actually use it and maybe buy the full version. Of course i don't really know what i ought to want in an RSS reader, so perhaps there are better alternatives out there anyways.
Pandora Radio (Free): You can sign in with your Pandora account and listen to all your usual stations. This is cool in theory, but i'm leery of using my phone for long term battery draining tasks like that unless i'm near someplace where i can recharge it easily. And if i'm near someplace where i can recharge it easily i usually have better music options available. (Pandora or mp3s on "real" speakers on my PC or audiobooks in my car.)
Music (Pre-installed): It's a perfectly adequate music player, and i like the way i can give it album images to display, but it suffers from the exact same problem as Pandora.
Aldiko (Free/$2): I've got the free version. It's an e-book reader. I downloaded a lot of free books but haven't read any of them yet. When i've got the time to read i'm usually at home, and i've got lots of "real" books that need reading here, along with all the other usual distractions.
ConnectBot (Free): An SSH client. It's perfectly adequate, although i wish there was a way to zoom in or switch it to landscape mode. However trying to read and type unix commands on a touchscreen phone is a little annoying, and most of the time i'd want to check anything i'm near a computer anyways, so i only use this app in case of emergency.
SpiraDefense and VoidDefense (Free): An interesting variant on tower defense games. One has you building towers on a circle in the center while enemies spiral inward from the edge of the screen, and another has build towers in a ring along the edge of the screen while enemies appear at the center and spiral outwards (a little like a tower defense version of Tempest.) It was an interesting change, but kind of a one-trick (or i guess two-trick) pony. By the time i'd gotten to the end of the demo i'd figured out the general strategy and it didn't really seem worth upgrading to the full version. If you like tower defense games it might be worth trying out the demos though.
Age of Conquest (Free): A turn based strategy game. One of those ones where you control provinces, recruit soldiers, try to take over new provinces, etc. It wasn't very complex and after beating the demo scenario i wasn't sure if it was worth shelling out for the full version. Of course for only $3 or $4 perhaps i ought to give it a try just for the hell of it.
That's definitely not all the apps i've installed, but i think it's at least most of the ones i've used more than a couple times.