Here's a few of my favorite anime OP/ED that come to mind.
Requiem from the Darkness is a rather interesting horror 13-episoder in a variety of ways, but it also boasts a wonderfully jazzy opener and closer respectively that gives the whole package a strong memorability. Sexy, yet evil.
An upbeat jazz-rap opening number that stands out quite well in Eureka 7's already rather awesome soundtrack. Actually, anime done by BONES tend to have great music consistently, so perhaps its not too surprising.
Utada Hikaru is about as good as it gets with J-Pop, and this particular track, the opening single from 2006's
Ultra Blue, is no exception to that rule.