We were lucky enough to get a rental home that had curtain rods on nearly all the windows. Nicer curtain rods, too, I think. Not the cheaper metal rods that look like a really long C. These are quite functional, but not exactly attractive.
There were a few curtains hanging up in the living room and dining area already. I left the red ones for ones for now in our dining room but changed out the dark brown curtains in the living room for a lighter colored pair. It's really helped in lightening up that dark room. They're somewhat sheer, too, which also helps with letting in the light.
Our girl is of the age to want her room really, really dark at night, so not only did we find some cute black-out curtains in her favorite color, but we also layered them with a pair of brown curtains that were already here. Her room is really dark at night now! Never thought I'd see that day...
The boys also have a pair of room darkening shades in navy, but I can't seem to find a picture of that area of their rooom.
Adam and I also put up some curtains in our room. When I first bought curtains I was sort of going for whatever the cheapest option was, but Adam encouraged me to get what I liked so we could take them with us and use in our next home. Curtains can be seen as an investment.
You can even change the shower curtain to make your rental feel more personal!
As with everything you buy to go in your rental, consider if you'll use it again in another place, either your next rental or a home you buy. Curtains could make the transition. A lot of furniture will, too. You may not be making any money by renting in the way of home equity, but you can make good decisions in how you spend your money by buying for now and for the future.