One band that's often overlooked and is one of my favourites is Portishead. Fantastic trip-hop band, all three of their albums are fantastic. I would start from the beginning (Dummy) and go from there.
I think it doesn't help that they didn't release an album for 11 years and their last album was 8 years ago already, haha. They were a big name in the 90's, but you gotta keep that up.
If anyone is into post-hardcore/metalcore, I can really recommend
TRUST THE MEDIC. Their vocalist is incredibly talented. It's a shame they don't have that much stuff out, but the 8 songs or so they have out are really good. I especially like their
Shake it off cover.
I know it's weird to recommend Panic! At The Disco, because their (or his now, I guess) new album was #1, but I feel like their album
Pretty. Odd. is not as appreciated as I would like it to be. It's an amazing album, drawing influence from the Beatles, and Baroque music. Another song not on that album, or any for that matter, that I would like to recommend by them is
C'mon, the song they did with Fun.. I love the lyrics for it, as the singers both use Alice in Wonderland references, with the first verse being influenced by Alice, and the second verse being based on the Mad Hatter.
A Dutch band that I love, and gets a lot of recognition over here, is Racoon. They make really good music, and I wholeheartedly believe their singer is one of the best vocalists the Netherlands have. They have compositions with brass sections, such as
No Mercy, but also really catchy poprock songs (
Feel Like FLying, and acoustic love songs (
Love You More).