If it's a big bug in the house...I will kill it or put it outside, depending on what kind of bug it is. If it's outside I might ignore it, or watch it for a while if it's a really interesting bug. Except if it's a black widow, I always kill those so they don't breed and make more. Oh, and I always kill the scorpions too.
I live in the country, we get lots of bugs, some are really interesting. I found a stag beetle in the driveway once next to the woodpile, I was barefoot and almost stepped on it - yikes! I just watched it for a bit and let it go on it's way. It's the only one I've ever seen so I guess they're pretty rare around here.
In the summer we get these monstrous flying beetles sometimes. One year I had a couple of them that hung out on the screen to the laundry room window for a couple of days. They were big flat beetles, the big one was probably about two and a half inches long, the other one a little shorter. Every time I got closer than about 3 feet or so they would hiss at me. It was pretty entertaining, I left them alone and they eventually left.
Some years I get argiope spiders in the garden. They get really large, their bodies can grow to over an inch long and very fat. They are so beautiful, black and brown and white and bright yellow, very silky looking bodies. They are also interesting to watch - sometimes I'll have a dozen or so in a pretty small area and I will preserve their webs and basically leave them alone because they are so beautiful.
I never eat bugs intentionally - oh, except I tried chocolate ants once, they were spicy...but I'm sure I've eaten plenty unintentionally either in my sleep or in prepared food where I couldn't see them...I'm sure we all have...
Here's a tidbit to freak you out - spiders drink out of your eyes while you are asleep!! This is absolutely true, and twice in my life I have woken up with a spider straddling my eye. Bugs don't usually bother me but that does creep me out a bit...