Well there were no stitches necessary . . . it's a funny thing, they don't stitch you up when there's norhing there to sew. Turns out the reason the cut I put on my middle finger wouldn't stop bleeding was because i cut most of the top part of my middle finger completely off.
I waited for the bleeding to stop for about 2 hours. When it didn't even slow down at that point and I started to get a bit lightheaded, I thought it was probably a good time to go to the ER. They wound up numbing it with a needle and then basically cauterizing the wound with a soldering iron. The top of my finger is totally charcoal now. But at least it's not bleeding.
And I even got a tetanus shot to boot. I was probably due for one anyway...
I'll see if I can get a good picture of it (just the bandage, no gore).