While I get some simply annoying side-effects (cottonmouth, namely), the strongest side-effects I get from smoking weed are both annoying and enjoyable in a way.
First, I get very sensitive in the extremities; it's often the first sign of being high to show up when I smoke. If I touch my fingers, toes or face in an even slightly rough manner (unscrewing a beer bottle cap, for example), they'll "itch" strongly for a while. But that sensitivity is wonderful when I'm petting my cat or eating something with a fun texture (like jell-o), for example.
For me, another pleasant effect that is intense to the point of being almost painful is music appreciation. I think it's from using cannabis with DXM for a while, but now music is almost overpowering for me when high. If I'm listening to something very powerful musically, I'll get almost uncontrollable spasms in the legs, arms and hands. These make me look like a total idiot, but are very enjoyable when I surrender to them fully (I couldn't call it "dancing" though).
I also get racing thoughts pretty intensely, almost to the point where if I wrote down all the jokes I make up when high, I could make a humor show; it sometimes gives me the feeling I'm trying to swim upstream in a river of my own thoughts. But despite being sometimes overwhelming, I find that racing thoughts are one of the most enjoyable (and perhaps most productive) things of being high. I'd probably get high only for these.