I almost always carry a tent (bivi if solo) and a tarp when camping...Siltarps are the cat's meow, but a little pricey if you're looking for occasional use. I've also carried one of the silvered tarps (not the "space blanket" but similar) on some trips...depends on weight etc.
I've hootched it here on the West Coast, even did the West Coast Trail with a fellow mbr and we brought our shelter halves and issue bivi bags with lots of success and some funny looks ??? You're going to sleep in that!?! Still had an extra to cover our rucks with overnight.
If in the mountains, I always bring a small 3- or 4 season tent, it can get pretty ugly trying to stake out a bivi on a rocky shelf, so the freestanding tent is my choice, 2-3 person size maximum so you can use a smaller clearing/shelf/ledge/flat spot.
Many times I see people set up a tent, and then set a tarp overtop of it...it's great if you're worried about UV breakdown of a fly on a long trip or base camp, but usually if they'd set up their tent properly, fly nice and tight, and taken care of the tent in the first place, it wouldn't be necessary.
I recall one storm where the rain drops were so heavy you'd see them hit the fly, pause, reform on the inside, hit the tent body, pause, and then reform inside the tent....not a pleasant night. I've also seen the 4-season "bombproof" tent turn into a bathtub because buddy was too lazy to stake out the fly, but the bottom was still nice and waterproof.
Hope this helps, watch out for the bugs up there!
DF