The asset store is full of stuff... Some of it useful, most of it is crap or won't play nice with other assets. My preference is to avoid assets that run with the game and rather to focus on assets that are tools to build your game. Below are a most useful assets I've used - some do run during the game.
Assets I've Created
I got tired of manually changing all the setting in my UI. Want to change the tint of all your text? That can take a while unless you define styles and then it's easy!
Click to Add is a very basic asset addition tool. It allows some level of "randomness" in asset placement. If your looking to create a small to medium scene this can be a pretty useful tool. Nothing fancy, it just works.
Unity doesn't currently allow rebind of keys at runtime. So I wrote a little program to help. Currently supports keyboard rebinding, but not mouse or controller inputs.
Assets I Use
I use Gaia to create my terrains in Unity. I then export an OBJ file to Blender where I do the final editing, texturing and exporting as an FBX. This allows hard edged terrains to be created giving a low poly appearance to terrains. My low poly terrain workflow can be seen on my YouTube channel.
Gena Can be a bit finicky to use, but once set up correctly allows very quick scene building. This is a must if you are a small team trying to build a large scene.
Behavior designer allows easy creation of behavior trees to create a wide range of AI.
Tenkoku Dynamic sky is beautiful. There are a few hiccups here and there, but it quickly and easily adds great visuals to a scene. Sunrise and sunset in particular are fantastic. If you're looking for atmoshperic scattering or a day night cycle this is worth a look.
There is no quicker way to adjust the lighting and color of a scene than with LUTs. Amplify Color will do it quick and easily with just a tiny performance hit (0.05ms of my desktop).
G2U is a database tool that allows you to store you data in a Google spreadsheet and quickly import the data. Fantastic tool if you game has lots of data (enemies, inventory, etc). Well worth the cost of admission.