With all types of diapers- prefolds, fitteds, pockets, all-in-ones (or twos), and covers- there are a variety of closure options you can choose. There seems to be a variance on personal preference when it comes to these choices!
Snappi fasteners can be used on prefold diapers or fitted diapers that don't have snaps or velcro. The "teeth" are very sharp and can grip the fabric. They are NOT to be used without a cover, because the baby could grab them and get poked by the very sharp prongs, and believe me- it hurts- I learned from experience! But they're quick and easy once you get the hang of them. Here's a link to a Snappi:
http://www.bananapeelsdiapers.com/catalog.php?item=286&catid=101&ret=catalog.php%3Fcategory%3D101 (Thanks Heather at Banana Peels!)
Pocket and AIO diapers either come with velcro or snaps. Velcro is more adjustable in most cases, but tends to wear out faster. And then there's the issue of "diaper chains" where the velcro comes undone in the washer and the diapers all stick together and become a chain. But velcro is easy for dads and babysitters and anyone else who prefers to put a diaper on quickly without hassle! It's also easy for toddlers with busy hands to figure out, so there's always that chance of having a little diaper-free streaker running around your house! :D
Snaps are on some pockets, AIOs, and fitted diapers. The benefit of snaps is that they last longer than velcro, and also are harder for babies to learn to take off. The drawback is that on some diapers, it's hard to get a good fit if the snaps aren't placed well- one setting might be too loose, but the next setting is too tight, so there isn't a good adjustment- which can lead to leaks. I personally prefer snaps to velcro, but my husband gets frustrated by trying to put snapping diapers on- and on more than one occasion, I've had to re-do the snaps on diapers my husband has put on. ;)
Pins are used for prefold or fitted diapers. There is something so wholesome-feeling about using pins. If you get the hang of them, they create a very customized fit for the diapers. The drawbacks... well, the fear factor! The fear of sticking the pins into your baby or into your hand can be hard to overcome! But hey, for reasons that are hard to explain, pins just make me happy! :)
I have diapers that have velcro, some that have snaps, and some that I use pins with. Having a variety keeps me from getting bored... or something. ;)