I'm at the coffee shop writing this, but a friend of mine asked what she should install on her Android device to make it more powerful and good looking than the default OOTB experience. None of thse require a custom ROM, some require Root. I'll add play store links when I'm not writing this over SSH on my transformer.
A lot of people say that root isn't necessary, but it opens up a lot of really great doors. Install a 3rd party recovery tool like TWRP and it's easy to gain root.
Created by an ex-Android designer, this is a really extensible locak screen and homescreen widget which can display information from your email accounts, show missed SMS, and a tonne of other things. You can find a bunch of plugins on the Play store, and a lot of apps bundle widgets in their apps these days.
Nova is a really customizable yet pretty standard homescreen replacement. Supports arbitrarily sized grid of icons and widgets, custom icon packs, and is just very well done.
This just got bought by Yahoo!. Basically it's a homescreen that changes throughout the day. When you're at home, it may show netflix and games, but when you're out, it'll show you transit apps and google maps. When you're at work, it'll show you your work email, etc. It's not nearly customimzable yet, and it doesn't support custom icon packs, but it's still pretty neat. Not a fan of how it requires a 3rd party server to do the geofencing though.
There are a tonne of these, some are free, some aren't.
This is what iOS7 icons could have looked like if they didn't look so garish. Rounded squares, really vivid colors, while still showing the original icon's intent very well.
Monochrome white icons sitting on translucent squares. Really nice with textured wallpapers
Android has a style guide for icons, but no one, including Google follows it. HoloIcons rethinks a ton of icons as a more native android design. I really like this one.
Llama is free and imo easier to set up, but both are basically a way to wire up profiles that can be triggered by different events that happen in meatspace. For example, silence phone notifications when my pebble is connected since those get delivered to my wrist. Or when I open up my sleep tracking application, silence everything except for phone calls from my family and PagerDuty. Turn on wifi when I get to work/home, and turn it off when I leave work/home.
Tasker is a lot more extensible, but a lot harder to get used to. I'm still trying to figure out the best way to port my llama profiles over to it, but it's also much more powerful, with a plugin API that 3rd parties are actually using. It can get wired in to MTW and Google Now (through Xposed below), and is just very intriguing.
Minimalistic Text is a bunch of widgets that do exactly what they say. Show text based on variables such as time, date, calendar entries, and anything you can feed it from Tasker. Text elements are highly customizable and you can set it to open up any application activity when you tap the icons, so I have a weather text on my homescreen which opens Hue, for example.
My friend Robbie turned me on to this one recently. Basically it's a mod framework that exposes a bunch of things that could generally only be done in custom ROMs like CyanogenMod. As a result, I can run stock AOSP and still have cool things like the extended QuickSettings tiles, screen recording, fitbit sync, AppOps, etc. You just need to root your device and install their framework installer. Lots of rebooting to enable things though.
And since you all use this thing:
Beautiful weather app that really hits holo design guidelines really nicely.
Prey is a multi-os open source theft prevention tool. Spend some money on it, put it on all of your devices. It's like android device manager but not tied to google, and not tied to android.
This little guy plugs in to your notifications and displays them over your lockscreen, with options to dismiss, or open the app, or even open other arbitrary applications like the camera. You can give them some money for some nice extra features, like pulsing the notification five minutes after, stuff like that.
What am I missing? What makes android shine for you?