Hmm... I usually make a point to watch the opening and ending songs of shows at least three times. Rarely, after that, do I watch them though. On the top of my head, I can only currently recall a few that I did, Higurashi's OP, Black Lagoon's OP, Susumu Hirasawa's are a must, and I also like most of Yoko Kanno's music when she plays a part. For some reason, I actually don't like ALI PROJECT. It's not that I dislike the music, it's just that it ALL sounds the same. If you've heard the Rozen Maiden OP/ED, you've heard the .hack//roots OP/ED, Code Geass ED... etcetra.
Really, when I DO have a song that I like, I usually find it and play it over, and over, and over, and OVER again. For like... days, until I'm sick of it. Then forget about it on my harddrive for months (or more) until I pull it out again and repeat the process. ^^;;