Before infusions with Remicade, people are often given antihistamines like Benadryl to help with potential reactions! But otherwise, Remicade is one of the older biologics. If I'm remembering right, it was originally made from mouse protein -- so it's the biologic people are most likely to get reactions to, since it's recognized as foreign. That doesn't mean you'll get a reaction, though! I have a friend who's been on it with no problems for maybe twelve years.
Other biologics -- like Humira -- are humanized antibodies, so it's much less likely you'll get a reaction.
That said, things I've reacted to:
Remicade (I built up antibodies to it very quickly, so it really didn't do anything. I would get bad eczema, especially atopic dermatitis while I was on it.)
Cipro/Flagyl (a whole whack of vestibular, neurological and cognitive symptoms that stopped after I stopped them)
Doxycycline (my dermatologist told me it had less side effects than minocycline, but I had uncontrollable nausea/vomiting with this. No issues with minocycline.)
Triptans (Can't remember which one I took, but I couldn't breathe! It was a little terrifying.)
Otherwise, the only thing I really get a reaction to is medical tape. My skin gets inflamed and breaks out with rashes immediately. It even wakes me up because it's so painful. (I've woken up after surgeries to realize it was used on me way too many times.)