Apps to get
I have had the OG for about 10 months, and rooted about 9 months ago. Here are some apps with a brief description to see if they're what you want:
APPS:
Act 1 Video Player - a great video player if you want to watch movies or anything, has great quality and features
Kindle - eBook reader, free
CacheMate - ROOTED ONLY allows you to clear all app caches to free up space
Dropbox - Allows you to share files between PC, phone
ROM Manager - ROOTED ONLY allows you to swap ROMS, themes, etc, but PLEASE READ UP ON HOW TO DO THIS as there are lots of nuances and things that could go wrong if you do things out of order or forget to back up
Google Voice - excellent FREE replacement to Verizon's visual voice mail, will put your voicemails in text form and you won't have to listen through 30 voicemails to find your most current.
Titanium Backup - ROOTED ONLY allows you back up apps (again great if you swap ROMs on a weekly basis like I do) also saves app data and will link restored apps back to the market so they can update. PAID VERSION allows your to clear the Dalvik cache, which can free up more precious space on your phone. I do this one every couple of weeks.
Root Explorer - ROOTED ONLY this is a great file manager (like Astro) that allows you to access files on your SD Card, but also allows access to your /system files and such to further modify your phone. Also read up on this as this can cause harm to your phone if you don't know what you're doing. Search the forums for further information.
SetCPU - ROOTED ONLY allows you to manage overclocking of your processors BUT REQUIRES AN OVERCLOCKED KERNEL, again, search the forums for this information as there are a lot of kernels that can do this.
MusicPlayerPro - This is my personal favorite music player, has great widgets, a lock screen widget, is clean, smaller, and has fantastic options for organization if you're like me and don't have a ton of your songs listed under a particular album.
Urbanspoon - a food finder app, great if like me you and your girlfriend can never decide where to eat or live in a place with lots of small family owned restaurants
Terminal Emulator - ROOTED ONLY (for best effect, not sure if its required) Allows you to run a CMD prompt to have further functionality on your phone, need to understand or be able to Google commands
SwiftKey - a great keyboard replacement
QuickBoot - ROOTED ONLY allows you to quickly reboot, or boot into recovery mode to do adjustments to ROM or system
Shazam - Allows you to use your phone to identify that song you're hearing in your car, store, or on tv.
TeslaLED - Uses your camera LED light as a flashlight
Wireless Tether - ROOTED ONLY allows you to use your phone as a mobile hotspot
AudioManager - you can set the volume of ringer, notifications, phone calls, alarms, etc from one place.
GAMES:
Abduction - A jumping platform game
Alchemy Premium - A very unique game where you match basic elements (i.e. water, fire, earth, air) and they form new elements, which then can be combined to make further elements. 360 so far.
Angry Birds - if you don't know/have this game, something is wrong with you.
Fruit Ninja - See above
JetCarStunts - a great time trial game, 3d graphics, installs to SD card, similar to free PC racing/TimeTrial game
MiniSquadron - A plane dogfighting game, fun, simple, but is a large game, even on SD
Need For Speed Shift - Was only $.99 on market! If still that price, is a huge game for the money!
Speedx3d - A 3d tunnel game, tons of fun, great controls
Toss It - Through paper (or an i*hone) into a garbage can
WordUp! - a fun scrabble, word finder game
Any of the retro gaming emulators - SNESOID, GNESOID, etc, allows you to set up your phone to play NES, SNES, Genesis, Gameboy games on your phone. Google ROM policies to avoid bootlegging or piracy. Best on phones with keyboards (to assign controls to it) but will work with virtual buttons on any phone.
TASKILLERS ARE NOT NEEDED, however, I do have one on my phone to help kill apps that go bonkers on me