General rules
Attacks on sleeping targets will break sleep.

Direct DOT casts on sleeping targets will break sleep. (SMNs in particular like to debate this.)


Things that won't break Sleep
1) SMN using Bane to spread dots from main target to sleeping targets.

2) BRD's circle of fire effect on the ground. (Don't know what it's called.) This is the only DOT I know that doesn't break sleep if applied after Sleep is already cast.

3) If DOTs are already ticking on a mob, and you add Sleep, CC will hold. (You can sleep after dots; you can't dot after sleep.)