My dd has one "best friend" a few months older than her, who she loves -- they have been playing together for about a year, but only recently started playing with each other
(talking, pretending, tickling, sharing food.) Up until about 4 months ago, they were happy to see each other, but then would do parallel play with some toy showing-off and trades.
My dd is VERY social, and is now in a class/ playgroup for 2-year-olds (think Gymboree, but cheaper and offered by park district). She will go right up to another kid and sit down next to them, look interested in what they're doing, etc., but the kids tend to grab their toys possessively and back away.
: She's getting good at getting their attention with games, though -- chase, play kitchen, etc. I think it's been really important for her to have these socialization opportunities for the last 4 to 6 months especially, but going back to when she was about a year old.