Are there any HDs that do not have a powercord and are powered through USB2 or Firewire instead?
Most 2.5" HDD enclosures that I’ve seen are powered off USB - you just need to get a laptop drive to put in them. It’s definitely more convenient, and much more portable.
Yes. Other World Computing, for example, offers a “bring your own disk” case for the 2" ATA drives that are ubiquitous in laptops. You can run those on bus power alone, with no power brick.
Finding an external case that will run a 3.5" drive is a bit more difficult — those drives have a bigger appetite for electricity.
To add to what others have said, generally speaking laptop hard drives (2.5") run off of 5V, while fullsize drives (3.5" hard drives and 5.25" bay optical drives) run off of 12V.
The USB connection only provides 5V as I recall, so that’s why you can use it to power a laptop drive but not a 3.5" drive.
You have to watch out, because some of the bus-powered drives teeter right on the limit of power demand and some USB interfaces are better at dealing with this than others. Although I think this problem is generally on the retreat.
My sister recently got a 60GB external drive that was powered off the USB. I thought it was curious.
I have an 80GB drive like that – it’s called an iPod. 
Most of the ones I’ve seen that are bus-powered are labeled as “portable.”
Mad Dog 2.5 enclosures have a supplemental power cord that runs off a second USB, for those occasions when your single connection bus isn’t cutting it. Very handy, actually. I have never used their 3.5 but it may work in a similar way.
I have some drives that come with one of those; you have to plug it into a different USB root hub though - as the power limits are per bus, not per socket. You can plug it into another computer to draw power and it will work because the cable provides a common ground.
Note that all the suggestions thus far have been USB. FireWire (aka IEEE 1394) ports don’t generally carry power. Apple adds power to theirs (early Mac iPods were FireWire, and powered from the port), and you can get powered port cards for Windows, but it’s not particularly standard. So if you’re looking for a self-powered FireWire drive, you’ll probably be out of luck (and at the least, look toward drives sold for the Mac world).
Fujitsu’s Handydrives are available in FireWire versions.