I actually listen to a fair bit on my laptop and my phone. Though i will admit, my collection is far more game based than it is anime based. However, there are a few soundtracks i feel weird not actually carrying about with me.
Cowboy Bebop OST - i don't honestly think i've found a better soundtrack to listen to that suits me. I still get a kick out of listening to most of the tracks, be it Go Go Cactus Man, Space Lion it's always good. I have a soft spot for Road to the West as well when i'm travelling or writing.
Redline OST - Ayase picked out easily one of the best tracks from the soundtrack, Yellow Line. I think it has everything, and it's fantastic in the way that, it basically tells you the entire story of the race at the start of the film. Each character has their own theme in it, and as it reaches the climax, you get the music starting to blend together. I'll admit, i have a thing for music that can tell a story. Of course, Lynchman and Johnny boy is cool too, and i have to bring up Redline day as well.
Eureka Seven OST - it's been a while since i gave the whole thing a listen, but some of the tracks really stand out. Most notably
Get It By Your Hands by Hiroshi Watanabe. It really captures the style the series went for.
Macross Frontier - The second of Kannos works, and i'll leave the others out for now. i could easily bring in Wolf's Rain, Escaflowne and more recently sakamichi no apollon, but i'll bring up this one as i don't feel it gets as much notice as it perhaps should. More pop in style than other macross i believe, i've not really covered much else yet so i can't say, but it's good all things considered.
I'm not entirely sure what others i can really bring up, but other notable soundtracks that have invaded my music collection are the likes of
Berserk - Susumu Hirasawa still is one of my favourite artists, this leads onto the movies as well, though he did only do the opening for them i believe. Others like, Space Brothers, Paprika and Gintama for it's comical OST all deserve a mention too.
As for openings/endings, they do litter my music collection as well, and i could pick out favourites, but i feel full OSTs are a bit more interesting.