I'm kind of envious of the people who can decide their favourite soundtracks right off the top of their heads. To be honest, I find picking a favourite out of everything that I've watched to date to be extremely difficult, simply because there are so many great soundtracks to choose from.
There are anime with beautifully composed instrumental music. For example, any of Makoto Shinkai's works, namely 5 Centimetres per Second:
Along the same lines, the ef series, anime and games included, also had beautiful soundtracks, which is no surprise considering they were composed by the same person who did 5 cm/second's soundtrack as well (Tenmon is a genius):
Another anime that had an amazing soundtrack, which I'm sure people like Nis or HeeroYuy would agree with, had to be the Kara no Kyoukai series. At times the music would be odd, dark, and creepy, at other times it would be peaceful and beautiful, but the most important thing is the music fit every scene perfectly and totally enhanced the experience:
Full Metal Panic: The Second Raid was another case where every track was perfect for the scene, and for some they even added to the emotional impact:
On the other hand, there were shows that didn't hold strictly to the instrumental music, and had amazing and unforgettable tracks like Tengen Toppa Gurren Lagann's Libera Me from Hell, which kept everyone on IRC going for months.
Finally, there are shows that completely surprise me with their vocal tracks. Sora no Otoshimono, which I initially thought was going to be terrible, had great vocal tracks for the end of some of its episodes, though this may only be in my opinion.
There are many more shows that I'd like to point out, but I'm afraid that I've already made it a bit too lengthly, so I'll stop at that. It's a bit too bad I can't go on about eroge soundtracks, because most of my favourite songs come straight from Visual Novels.