Q:

Is there a way to get games I previously got on PS+?

On the PS3/PS4, say I remove a game I got for free via PS+. Is there a way to get back that game and redownload it?

A:

On the PS4, you should easily be able to see everything you have downloaded (even if deleted. This also includes disk-based games, as denoted by a small disk symbol in the corner) in the library via the main menu bar, far right side. There should be an option to redownload there.  
On the PS3 (and presumably also the PS4, although you have the above method for that as well) your download library is kept in the PS Store. On the left menu bar, near the bottom, there should be a "Downloads"* tab. Open that, and it should list every game you've ever downloaded, even from PS+.  
*I'm not 100% sure the tab is actually called "Downloads", but there is an option near the bottom to view all purchases made.

