Vital Side Skills in Skyrim

Throughout my travels in Skyrim, I would always find myself in a situation requiring a high level in a skill I didn't invest in. For example I'd need a level 40 alchemy to create a potion but put your skill points into lock picking (I actually think alchemy is a useless skill in my opinion). But I think one of the most important side skills in my opinion would be lock picking, restoration, speech, sneak, and smithing. The ones not on the list is utterly useless to me or I have not bothered to look into.Feel free to object in the comments!