Recently, I got an HTC One, and after rooting it I finally got everything tweaked the way I wanted it to. I ran across a few great apps that I didn't know about before, so I though that I would share. :)
The first on the list is called List My Apps. I'm probably going to have to wipe my phone in the future, and this little gem allows me to export a list of all of my installed apps. Even better, I can export in HTML with links to the Google Play store so I can reinstall them easily.
I ran across an amazing anti-theft app called Cerberus. I really like being able to control my phone via the web.
Night Mode is a tool that turns your screen's brightness WAY down, so you can glance at the screen in, say, a dark movie theater without it being annoying to other people. Be warned, it's so dim that if you try using this when you aren't in a dark room you might have trouble getting the phone back to normal!
Swiftkey is another 3rd party keyboard that can look through your Gmail and Facebook items and learn to suggest words based on how you text. It's uncanny how good the prediction is.
SwipePad allows you to set a hotspot (or multiples) which opens a 'dialer' type interface to start a shortcut. For example, if I press in the upper right side of my phone, I can then drag my finger down and choose between a number of items - call my wife, start a program, etc. There are various extensions you can or need to buy for certain functionality, but this app has served me very well.
Timely is an absolutely beautiful stopwatch/alarm clock app.
I like to automate my phone, so I use Locale to change settings based on my location. When I'm at work, my phone goes to vibrate only. If I go to the grocery store, GroceryIQ starts up and my phone changes to not turn the screen off, etc. That really helps my battery life, because I keep my wifi off unless I'm somewhere I know I can connect, or I connect manually.
I FINALLY found a good program that I can use to stream things from my media server at home to my phone. I only use this on the network, but it's called Emit, and it works great so far.
I use FolderSync to sync up files on my local filesystem every night while I'm sleeping. I use KeePass to keep my passwords at home, and only ever edit the master list on my computer. At night, FolderSync downloads the the KeePass file from my PC and overwrites yesterday's copy on my phone. I always have a copy of my passwords should I need them. I also use it to copy pictures to my file server. I use the cloud too, but Google/DropBox/etc. doesn't care about my files, and if I don't take care of them they might get lost. I don't completely trust cloud storage providers yet. I use them, but I still do my own backups.