I like to work semitone double-stops into my improvising. They're best on the 2nd and 3rd strings, as I don't have to stretch as far. Sometimes I hold my fingers three frets apart in semitone formation and slide around while strumming like a spaz. That's my Nels Cline impression.
When I'm not shooting for crazy, using these semitones requires knowing where the good ones are. Here are a few I try to use:
maj7: #4/5, 7/1
m7: 2/b3, 6/b7
7: 1/b2, b3/3, #4/5, 5/b6, 6/b7, or random pair
m7b5: 2/b3, 4/b5
When working these into my playing, I might pause between melodic passages to hit one, or I might play the two notes sequentially and let the first note bleed into the second. They sound particularly nasty when I bend the lower note up just a tiny bit for extra dissonance. Those needles in your ear turn into muddy hammers as you explore lower registers.