Obviously Facebook, Gmail, yahoomail, etc. if you use those. Google Maps and Google Nav (free GPS) are key. Google calendar works well and has a nice widget. ESPN Scorecenter is cool and has a nice widget, make an account and note all your favorite teams and it makes it very handy for checking scores, game times, quickly getting box scores, etc. NFL Mobile for Verizon is dope and the regular NFL Mobile app for all carriers seems good too. The one on verizon lets you watchh Redzone channel and a few other NFL type channels and get radio feeds on your phone even for local games. ebuddy is good for FB/AIM chat. Chrome-to-Phone is pretty handy too. Install it on your droid and install the extension on chrome (I believe it exists for firefox too) and whatever you're viewing on your computer browser you can send instantly to your phone. Especially useful for directions I've found as its much easier to look up google maps/directions on the computer and once you get what you want just send it to your phone and it comes up on the google maps app. Google Voice is pretty dope too. Has a ton of different features- you can get a whole new phone number from google and tie all of your other numbers to it and set different settings for what phones to ring depending on who calls. I use it only for voicemail as I have unlimited calling anyway but if I was more tech savvy/trustworthy I'd get a cheaper cell plan and just use the free google voice number. Mostly its useful because it converts voicemails to text and texts them to you and also posts the transcriptions in the app and you can play/pause voicemails and they're all saved much more neatly in google voice than standard voicemail. Transcriptions are pretty hit and miss depending on the person's voice though (I believe its still a beta product). Listmaster is just a simple list making app but useful for people with horrid memory like myself. Realcalc is an awesome scientific calulator if you're a student like me. Mototorch lets you use your camera LED as a flashlight which comes in handy and has an easy-to-access widget. Advanced task killer if you're a task killing addict like me. Dropbox is nice but I rarely use it. Don't use my droid for media much but I like doubletwist for that, has a computer program with sync very much ripping off iTunes. Movies is a clean app for checking out showtimes and just general movie info, IMDb is ok. Amazon is ok. I have "SF Baseball News" which compiles a list of daily news articles on the Giants and "Raiders News" which does the same for the Raiders. Redbox codes is simply an app where people upload codes that get you free rentals at Redbox and then people post whether it was successful or not for them, the result being a good resource for getting free rental codes (though I've found redbox limits how many you can use per credit card or email account or something). I use Launcherpro instead of the standard look. Actually not sure if its better than Android 2.2's new interface but I still like it a lot. As for games- Angry Birds is pretty fun, Unblock Me is an addictive puzzle game, Trism = tetris, aTilt and Labyrinth for Labyrinth games, Frozen Bubble = bust a move, Baseball Superstars free is a pretty fun little baseball game, I was fuggin HOOKED on Coloroid for a while, Homerun battle 3d is kinda fun, and then you got tons of options for Chess, Texas Hold Em, solitaire, blackjack, etc.
Get the GameBoid or SNesoid. They're emulators for the GameBoy and Super Nintendo and there are hundreds of games available for them for free.