Is it possible to capture video from a dvd using my computer's DVD drive through Adobe Premiere Pro?

You can either use a ripping program such as DVD Decrypter to rip the VOB files and then convert the AC3 audio and bring it into your NLE OR you can use a stand alone DVD deck, hook it up to your computer thru the firewire and capture that it that way.

Most NLEs won't read the AC3 audio file and AFAIK most DVDs use the AC3 audio file
You can find audio conversion programs on Cnetdownload.com-there are a few good ones none free that I found but they are pretty inexpensive.

Don

OR you can use a stand alone DVD deck, hook it up to your computer thru the firewire and capture that it that way.

Better look very carefully at the specs for your DVD recorder before assuming that this is possible. I bought a Sony RDR-GX7 a couple years ago so I could make quick and easy DVD dubs. I looked at just about everything on the market back then, and none of the consumer models had firewire output. The firewire port is for input only. So you can connect the DVD recorder to either a camera or computer via firewire and burn a DVD, but you cannot send video from the DVD recorder to a camera or computer.

Perhaps some of the newer models can do this now, but I haven't seen one...