Hmm, well with my first betta, I would sometimes put my finger in the water so he could nip it. It tickled and it was super cute, but I was dumb for doing tat, so I don't suggest you do it. It's super cute, but still....
No, I have never "pet" my betta.
And as others have said it's bad because you could have soap on your hands and if you do it alot you will damage the slime coat. Letting your betta "nip" your finger once in a while is OK just make sure your hands are clean and have NO soap on them.
I wash my hands vigorously with hot water (no soap) for a good 2 minutes before touching anything fish-related. I brush my goldies' mouth... They love it. Whenever I am cleaning their tank, they would slalom between my fingers. I've "grabbed" them by accident, they only freak out because of the suddenness of it (I'm usually grabbing deco).
Also, one of my goldies has a vision problem so I have to hand feed him. Just be careful and sanitary.
I have not done any of this with my bettas, though.
I would say that it is much safer for goldfish, koi, etc than for bettas. They just are not big enough fish. But when you have a 1ft-2ft goldfish or koi, you are a lot less likely to damage them. They also would be more likely to enjoy it because a hand is closer in size to them than it is to a betta. I image a hand to a betta seems like a predator.
I don't know that I would ever seek out to pet my fish, but I don't think they are nearly as delicate as they are made out to be sometimes.
@Kytkattin: I don't know if my hand seems like a predator to my bettas at least. When I go in their tank with the siphon for water change day (I leave them in there) they are completely fascinated with it and follow me around.
My betta stares at my hand. =/ If he thinks I'm going to feed him, he jumps. o.o.. He's bit my finger a few times. It doesn't really hurt; it kind of tickles. Lol. He's eaten from my finger before, too; it feels so weird (in a good, adorable way). Are betta mouths essentially vacuums?? Have you seen them eat larger pieces of food? o.o Their mouths like...extend..
Lol! Definitely. I don't spend too much on food for Turbo. He has his pellets, flakes, granules, freeze-dried gammarus, freeze-dried bloodworms... Lol. He doesn't eat much, though, because he's really small, and he has a super-tiny mouth. I give him the granules daily (unless I fast him or give him a gammaru). Sometimes, I even have to break those in half for him. =/ So little!!! He doesn't get flakes much at all, but it may be easier for him to eat them, because I can break them up for him. =] I've not given him any bloodworms, yet, though.. Nervous about how they may make him bloat. He loves the gammarus (baby brine shrimp)!!! o.o