When receiving a compliment, my favorites are the ones that come from people whose opinions matter to me, or who have an insight that either surprises me with a positive or happy view of me or confirms/reflects something I already think (and like) about myself. Compliments from someone whose opinion I don't particularly respect don't carry much weight and even, on occasion, make me feel vaguely disappointed or put-down. On the other hand, when it's someone whose opinion I value and who "speaks my language" and can compliment me in those terms, that's just about the best, topped only by the compliment that's completely unintentional: the statement that isn't intended as a compliment but because of its delivery as a statement of fact or simple observation, carries that much more weight.
In general, it's great to receive a compliment, of course, and despite the dangerous size of my ego, rarely, if ever, do I turn them down (unless they're those backhanded compliments, like, "You look so great these days!") I always, though, feel weird about compliments on my looks. I mean, of all the things about me, my looks are the thing over which I have the least control. I mean, yes, I have fabulous curly hair, but, well, that's pretty much just genetic luck, so I'm never sure quite how to respond to that sort of compliment. On the other hand, having my looks admired is pleasing. Almost all of us do, after all, want to be attractive, and it's satisfying to achieve that.
The flip side of that is that it's incredibly hard for me to compliment someone on her or his looks. I might say something like, "You look fantastic!" or other general things, but it's very difficult to say something like, "You have beautiful eyes," even if that's what I'm thinking.
I also tend to think that if someone is very attractive, or, more generally, has some great quality worth complimenting, that they probably know it already, and so it often doesn't occur to me to say anything about it, since I hate stating the obvious. This is probably silly, because, really, everyone likes a compliment, right? Still, it's an ongoing struggle for me.
Also, sometimes, for reasons that I haven't entirely teased out, I feel vulnerable complimenting someone, especially on some feature of his or her looks. I'd say more about that, but I really don't know what it's about.
This comes up from time to time when I find myself thinking lots of good things about the people around me and that makes me happy, because I love being with people who make me think good things about them, and then I realize that I haven't said anything about it. Silly me. Then I do one of those compliment memes and I get to say good things about many of you, which I like. I'm going to try to do that more, though, and unprompted, because I really do like thinking and saying good things about my friends. It makes me feel good, and it makes them feel good (I hope!).