I'm another person that doesn't really know about a film's budget before I go see it. I mean obviously I'm aware when something's a blockbuster, and sometimes it's pretty obvious when a film was made for less than my annual salary. But unless the budget is really apparent in the film (in the aesthetic, usually), I don't give it a lot of thought. When it is apparent in the film, I judge it fairly neutrally--it can help, and it can hurt.
I will say that I think I'm more likely to notice the budget as a factor when it works, than when it doesn't. When a small budget hurts a film, I'm probably likely to call it ineptitude (rightly or wrongly) rather than strictly pinning it on the budget. And when a large budget hurts a film, I'm likely to call it over-indulgence (rightly, probably). When a small budget lends a fitting simplicity to a film, though, I may notice that. And when there's some appropriately breathtaking scene in a film that could only have happened with a lot of money, I'll probably notice that as well.