I've got a number of apps that I've installed but only so many I actually use...
Remoting into other computers:
TeamViewer - for when RDP doesn't want to cooperate.
ConnectMe - RDP client, kinda works...NetBIOS names seem to break on WP8.
Music&Video:
onePlayer - a decent DLNA app that kinda works (its really a WP7 app, Nokia's PlayTo does the opposite of what I want; I loved HTC's Connected Music app for WP7)
ModPhone7 - Plays tracker music (MODs, XMs, ITs, S3Ms)
WOMP - Also plays tracker music, it was the first in the store to actually work.
Sat Rad Player - An app that plays the streams from SiriusXM. Its no longer in the store AFAIK...
MPAtool - used to be homebrew for WP7, but its officially a legitamate app now. It mostly adds images from last.fm, but does a basic google image search too...
Games:
Tiny Death Star - A freemium game thats actually playable without throwing real money at it.
VGBC/VGBA/SNES8X/EmiGens/EmiPSX - Emulators that I use to kill time in public. Sometimes I wish they made a shell-like moga controller (I don't actually use these too often where I'd want to purchase one, but not all of these have support for it either...)
Internet Stuff:
UCBrowser - A "private" browser that has previously had a homebrew version for WP7. Also works for downloading stuff that IE wouldn't download.
Amazing Weather HD - Nice live tile.... Thats about it. I solely use this to check the weather. (Radar is meh in all weather apps in the store.)
SysApp Pusher - A must have for checking updates and installing apps for other OEMs.
Skype - I occasionally chat with other xda members using this, but it doesn't always work in the background.
Zinio - I have a few magazines I read using their service. Namely PCMag....
MetroTube - Some might actually object to this, but it just has always worked for me. I also had this on WP7 a year ago. I download some youtube videos using this, but I'd wish it had a transfer to music+videos option to watch it on something else or to download them to the PC.
Gasbuddy - I used to try and report gas prices to help others, but since I'm the one who does most of the driving... its not very useful unless I need to find gas in the first place.
Windows Phone Central - This is kinda the only news I read anymore. Politics and regional news is the same stuff month after month.
Tapatalk - I post here using it when I need to just do a quick update on what I'm doing or if I can actually help someone.
facebook beta - Its facebook... what more can I say about it?
wptorrent pro - a torrent app that plays movies and stuff...it shares the files to the local network via a web-server.
Lockscreen background:
Lock Manager - a visually appealing lockscreen that I can live with that has the weather in a format that doesn't take too much of the lockscreen image away.
glance background - added a monochrome version of Master Chief (John) from Halo and set it too look like it was on 8bit device
Mapping/GPS Stuff
HERE Drive+ - Annoying as h***, I use it mainly for my current part-time job and I'm beginning to feel extreme hate for it. The fact it mutes the audio when it announces things is the first annoyance instead of pausing the music or just ducking behind the music volume while announcing the directions. The second annoyance is that it doesn't announce the address right before I destinate. (at least after the last update it shows the hose number instead of just the street name.) Also, it doesn't always have the most accurate maps, its 3 years outdated in my region, so roads have been renamed and other roads have been outright closed. When not actually not on the road it tends to snap you to the road, so you could be in a parking garage where it snaps you to a road when you are actually on a different one. This app fully assumes that you are still heading the "proper" directions until it recalculates in ~5-10 seconds. All of this just makes me wish the Garmin app wasn't so darned expensive.
gMaps - I use this when Nokia Drive/Bing Maps/anything that uses the OS's maps are out of date and need to get to a missing street.
GPS Voice Navigation - I've dabbled with this a bit enough to say its nice to use, but requires data; navigating around the app isn't as straight forward as it should be.
Developer Apps:
TimeMe - a clock tile with the date, battery percentage and the current weather (just temp and status e.g. cloudy image and temp)
Native Toast Launcher - Used for launching hidden pages inside any app.
US MO Apps - for whenever I can get Fiddler to work right again...