What's this style of guitar playing called?...

[DanTheMan]

The sort of off-picking sound as though the guitar is being 'plucked', sounds a bit reggae-ish. Can be heard in songs such as:

10cc - Dreadlock Holiday
Steely Dan - What a beatiful world
Eric Clapton - I shot the sheriff

Also, can anybody recommend me any more songs/bands that use this style.

 

[Augmented]

If I'm thinking of the right parts you're referring to, that style of playing on the off-beat (or the upstroke, if you like) is typically known in as 'skanking'.

For example, in 4/4 you skip the first beat and play on beat #2 and #4. It's important that you partially mute the notes of the chord shape i.e. those on the bottom 3 strings, to get that 'chukka' sound.

http://www.youtube.com/watch?v=ptHsy6edEZ4 seems like a good starter guide. Note the first comment - you don't always need to play the chord with an upstroke motion, downstroke works well for a different sound.

 

[penski]

Check out the track Onscreen Rapist by Murder One for the best application of this ev0r.

*n