PC:
Pro:
No console can touch it's graphics quality. Seriously, not even close.
The latest and best technology in terms of both hardware and software.
FREE content (mods, demos, etc.)
FREE online gaming for most games (you've got to have a broadband connection either ways, why pay the extra $).
LOTS of games in all genres.
Greater control and more flexibility in game.
More customization capabilities.
MMORPGs, RTSs, simulation and empire building games. These genres are a joke on consoles.
Can be used for countless other things besisdes gaming.
and to quote Homer "It teaches you while you learn." I have never met a PC gamer with poor computer or typing skills. These skills are marketable in the workplace. No one is looking for people with console gaming skills...at least not if you want to make more than $7 and hour.
Con:
Cost (4-6x that of a console)
No rentals (plenty of free demos though, you just can't play all the way through without buying).
Complicated set-up.
High maintance to keep everything at peak performance.
Some times buggy performance (the reason for the last pro

).
Lack of a really solid controller (not sure why people even buy one, just use the keyboard and mouse).
Exessive Noise and Heat (all that power over what a console does produces a lot more heat and requires a lot more cooling).
Inability to play games with multiple people on the same machine.
Upgrade itis (costs more upfront and in the long run).
Consoles:
Pro:
Easy to set-up.
Easy to learn and use.
Can be used on almost any TV and sound system.
Lower cost.
Game rentals.
In game DD (Xbox only feature) (only a few PC titles offer this, not sure why).
Basically no maintence.
Can play with multiple people on the same machine and TV.
People of all skill levels can use and enjoy (you wouldn't want to let your 5 year old nephew play with your computer).
Lots of good controller options.
Con:
Can't be upraded, only replaced.
Extra cost for online play.
Gaming experience limited by hardware performance of several years ago.
Once you've played a game you're done with it. No mods or new maps or other user created content.
Limited support of online capabilites.
Limited support of high-def capable games.
I'm sure there are other things that could be added to all of these but this is what I could come up with right now. I'm sure some people will disagree with me but these are my opinions. I of course am a computer gamer and see no reason to purchase a console. If I was going to buy one though it would be Xbox because of its support of High-Def, in game DD, Hard drive and, the mother of all console FPSs, Halo (Halo 2 coming soon).