The standard wrist strap has the little alligator clip on it yes. Basically anything that keeps you in contact with the system or a ground connection will work. Even physically grabbing the case works. Also avoid working in area with carpet and don't ever work with socks on. HA!
Hope this helps...
I have decided it's time to invest in an anti-static wrist strap, as I have probably fried more than one computer by not having one. I assumed they were expensive but i see them with little alligator clips
for $5 at microcenter. i thought they cost more than that. is this a mickey mouse version or do they work? any advice on which one to buy? thanks - fj

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic