thongs: when you're wearing leg gins and don't want panty lines (if thongs are uncomfortable for you, you can buy seamless regular underwear at places like La Senza and VS.) Thongs, and just sexier underwear in general can sometimes give you a confidence boost at parties and such.
bikinis and cheekies: more comfortable then thongs, still come in cute patterns and stuff
those granny-like comfy cotton ones your mom nought you: the ones you sleep in, aka your period underwear, aka the ones you've had for about 4 years but somehow still fit, you wear em' with sweats and on those days you really wish you were still in bed
Yes, many women leak a little bit down there. It's more hygienic to wear underwear. You can choose to wear underwear or buy a new jeans every month. I choose for underwear, because my jeans are about a €100. It's also more comfortable, because some pants scrape a little at the butt area and the front area and underwear prevents that. You could also just wear a skirt, but it's often not warm enough to wear one (like in my country). So I actually wonder how you can live without underwear.