It happens a lot, you get to the end of an anime and find you want more story, so you seek out the manga or light novel that it was based on. I usually stick with the anime and avoid the manga or light novels until I know they aren't going to make any more anime or I lose patience. If I happen to read a manga first, usually I don't bother with the anime. For example: I've been reading Attack on Titan since it came out, but couldn't bear to start over with the anime since I was so far along (same with Walking Dead TV show). I don't seem to have the same problem with novels though, since I happily watch Game of Thrones years after reading all the books (though I have been avoiding Irregular at Magical High School spoilers from the light novel readers like the plague every week on Crunchyroll).
One of the manga I've picked up since its anime finished up is Claymore. The anime's ending deviates from the manga significantly. The last two issues of the manga though (149 and 150) have been positively awesome, so I encourage everyone to find a way to read it. The other manga's that I've started reading after completing the anime are Berserk, Shigurui, and Hajime no Ippo. I'm tempted to start reading the Noragami manga, but I think I'll wait on news if season 2 of the anime is happening or not. I'm also on the fence with continuing Spice and Wolf in light novel format, partly because I've never read a long form Japanese translation that worked for me as English prose.
So how about everyone else? Any anime's that you continued on with in other formats?