I supposedly have a six Megabit connection, and my ISP says I should get six Megabit down and whatever up (ups not important right now). Question is if I'm supposed to have a six Megabit download speed, 768Kilobytes, and I only get about 600-620KB at most, should I be concerned? Or does that sound about right for my connection and I'm just not figuring something into the equation?

Every download produces overhead, means traffic that is needed to check whether the downloaded packets were ok of not and initiats a retransmission if needed.
So you can see, every download causes upload, because your machine must tell the download server whether transmission was ok or not.
The faster the download, the more upload is needed to answer the download server and request the next packet to transmit.
It also depends on the speed of the server, you're downloading from.
So all in all you can say, the download speed of 600 to 650 (at a good day) is quite ok. It's a good speed.

But keep in mind, the upload is important !!!

E.g.: A 20 MBit line will not get full speed if the max upload speed is only 128 kbit/s.

Okay thanks, I knew there was something I was forgetting. By the way, my upload speed is 768kb, so I think my speeds are about right.

Anyways, thanks for the answer. :)