Moon Safari is great, it's one of my favorite chillax albums as well. And yeah, I also think 23 has its chillaxing moments even though Blonde Redhead is too much rock to be called a chillout band imo. Also, you really need to get 23, Shep. Blonde Redhead are playing here next week, I might go see them.
Man, there are so many albums I listen to when I want to chill out. I don't even know where to start or what to recommend but I can't really be bothered thinking about that now so I'll just say what I have been listening to lately.
Elsiane - Hybrid (
myspace)
I bet some people think this is gay because of the vocals (a bit like Joanna Newsom I suppose) but I have been listening to Elsiane's debut album Hybrid pretty frequently lately and I like it a lot. It's very relaxing and has a distinctive sound which I like. If you are into trip-hop/electronica/downtempo whatever this shit is called, you might like this!
The Cinematic Orchestra - Ma Fleur (
myspace)
Maaaaaan, I have loved this album ever since it was released last year and recently I have started listening to it more again. Even though there are some kinda average songs on the album, I still prefer it to Every Day and Man With a Movie Camera. Man, To Build a Home is so fucking good, it's probably one of my favorite songs ever. I really recommend this album.
Emancipator - Soon It Will Be Cold Enough (url=http://www.myspace.com/emancipator]myspace[/url])
Another trip-hop/electronica artist, not too similar to Elsiane though. I think it's a bit more chillaxing actually, and has less vocals and is more instrumental. I dunno, this album just clicked with me right away.
Alpha - Come From Heaven (
myspace)
Unfortunately their myspace only has songs from their newest album (I haven't heard) and Come From Heaven was released 10 years before.

Anyway, I just recently started listening to Alpha but I like what I hear, very nice electronica.
Actually I decided to post about a few other favorites too.
ANYTHING BY NICK DRAKE (
myspace)
Not sure if Nick Drake is what some people would expect when you mention chillaxing music but Nick Drake is very relaxing to me. It's just really soothing and whenever I feel like listening to something nice and chillaxing, Nick Drake is the way to go.
Saltillo - Ganglion (
myspace)
This is one of my newer favorites since I only discovered this album last year. To be completely honest, there are plenty of tracks which aren't really that chillout but even so, whenever I think about something to relax to, Saltillo is definitely one of the artists I think of! I have mentioned them before and I'll mention them again. Listen to the song Giving In on their myspace, it's awesome.
Ólafur Arnalds - Eulogy for Evolution (
myspace)
Going to continue with another recent favorite since this album was released in 2007. There's really not much to say about the music, it's just really beautiful music with piano. Ólafur Arnalds released a new EP this year but seriously, it doesn't even come close to Eulogy for Evolution.
Ulver - Shadows of the Sun (
myspace)
More 2007 albums. Shadows of the Sun was easily one of the best albums of last year. This is not going to be everyone's cup of tea because it's not the happiest music around and the vocals can turn you off but if you are into electronic and ambient music, at least give this one a try.
Ef - I Am Responsible (
myspace)
Needs some post-rocks. But Ef is seriously great, they have unique sound unlike 99% of post-rock and make really nice relaxing music. I'll say this first, Ef's best song is without a doubt Hello Scotland which is on their first album (it's on their myspace, listen to it) but since we are talking about albums here, I Am Responsible is way more cohesive.
I think Shep listed a few good ones too. Bonobo, Mice Parade and especially Landing are all good. I have Outside Closer by Hood and it's pretty nice but I haven't listened to it in a long time because pretty nice is the only thing which comes to my mind when I think about it. I have never really gotten into Tortoise even though I have tried, they have decent stuff but are mostly boring to me. I got an album by Blockhead too but I don't seriously remember anything about it so I'm going to listen to it later. Sufjan Stevens is good too but I never really treated it as chillax music in the least! Anyway, I still have many more albums which I like a lot but those are some good ones, not really my overall favorite list or anything though, was just naming albums which popped up in my mind.
Also I'm gonna check out Beach House.