Yes, I would say I'm more intelligent than average, though my confidence in that fact becomes increasingly shaken daily, along with how I define intelligence.
I got moved ahead two years at school in the UK, got straight As and A*s at GCSE, got straight As at A Level and am currently in my first year at a pretty good Uni. This might be evidence for my intelligence were it not for the fact - as others have pointed out - that academic achievement has very little correlation with intelligence.
I'm eloquent, polite, confident and have had a good upbringing. I used to do a lot of public speaking events and achieved Grade 8 at Piano. I don't think these really have a relation to intelligence either.
So I guess the reason I'd say I was intelligent is based on personal experience - conversations I have with people, where it becomes apparent that steps of logic that seem intuitive and straightforward to me require lengthy explanations for other people. That's probably as good a measure of intelligence as I can conjure.
That said, I have very little "common sense", am the polar-opposite of streetwise, and can't really be trusted to manage my own life with anything approaching basic competency. All of which makes me wonder whether I actually am intelligent or not.
For example, someone else in this thread raised the example of customers asking them the prices of items in a store, when the price sticker is clearly marked on the product. I make stupid, idiotic mistakes like that daily. Does that make me unintelligent? Is that a better or worse measure of intelligence than exam grades?
In short, I don't know. But I'm still self-confident (or deluded) enough to be inclined towards optimism. So for that reason, I'd say yes, based upon personal experience I am more intelligent than average.
