I'm a renter - I've never stayed somewhere longer than 2 years since leaving my parents house in 2006. Since 2006 (this is counting dorms by the way but not my parents' home) , I've lived in 7 different apartments/homes/townhomes, 8 if you want to count Jason's place in Orlando. Painting is not really an option - we know we'll have to paint again soon enough on our own dime. Hanging things on the walls is a scary thing. Even those special 3M sticky things can really ruin walls!
You know, wall stickers! Ikea sells them, Target sells them, and you can get them pretty cheap online. Occasionally, you can transfer from one wall to another with smaller designs (like birds). They are a great way to decorate and come cleanly off the walls.
Those standard, in everyone's place Ikea bookshelves are perfection for small places and for decor. I use mine as a 'table' behind my couch, as an extension of a desk for my printer, and now as a divider between 'rooms' in my townhome. They are the most useful things ever and take up a lot of space - which usually brings your eye to them and the cute things they have on them.
Using bright colors or bold textures as an accent is a fun way to make things more personal. For instance - my DIY colored sofa feet. Or a bright rug!
Prop Up Paintings
Get one of those bookshelves, and on the top, prop your paintings up against the wall. Or put photo frames in the bookshelf. It will give you the illusion of having something on the wall without actually having to put nails in the wall.
Banners, Bunting, and Garland
These are great - they can usually be put up with some shipping tape and do minimal to no (never damaged for me) to walls. Plus, they are easy to DIY. Here's my favorite one for garland via Maddie Richardson.
I'm sure there are many other ways to decorate your rental - please share them! This is just how I've gotten through the past few years.