I chewed betel nut many times when I was in Papua New Guinea on a research project. Everybody (including kids of 3) chews it there in the areas that it grows naturally. It has a kind of sour/bitter taste that I liked a lot. I usually just chewed it green, but a few times I chewed it with lime and daka, or betel pepper. A couple times stand out in my memory. Once I asked for a really strong betel nut and the local buai (betel) fiend gave me one. I chewed it up with a bunch of lime and daka. It totally made my head spin and it was a lot like the first time you smoke a cigar and forget that you're not supposed to inhale. I sweated a lot and I was kind of zoning out. Somebody asked if I was OK and I said 'Oh, mi spak nau' (Tok Pisin for 'I'm buzzing') Everybody laughed.
Most times when I chewed it with lime though I just got animated and chatty (not my usually speed, I'm normally a fairly quiet guy), sweated a lot, and generally felt up, like I'd just had a good strong unfiltered cigarette or cup of coffee. Overall I really enjoyed it. I think it's great stuff as long as you don't go nuts with it.
There were people with black teeth in PNG from chewing it constantly, and one guy I knew was clearly addicted. I wish I could find some in the states. It would be great every now and again. Also, I would love to see people's reaction when I spit a big stream of orange red betel juice!