TundraWolf said:
Short answer (regarding Crysis): no.
Long answer: Yes, but it won't be pretty. You would have to turn the graphics down really low, and, even though it will still look just as good as the high-end graphics on most other games, your computer will start to lag and freeze when you get to the bigger battles/end-boss.
I'm speaking from experience, as a guy who got an $800 computer and stuck a $300 video card and a $200 power supply inside. On the entire mission preceding the end-boss (and including said end-boss), I had to turn down the graphics to minimum on everything, and it still crashed my computer every time except one (the one time I beat it).
It really depends on how much you want to spend, though. If you have the money, I'd suggest checking out Alienware, as they are renowned for having the best gaming rigs in the business. I have heard good things from people who build their own, so that might be an option, but you'd need the know-how and expertise to get it done (or know someone/pay someone to do it for you).
Either way, though, to get a respectably decent gaming rig, you'll be looking in the range of $1500 to $2000, at the least.
Either update your drivers, dl the patch or run a 32 bit os. That's your top 3 solutions to games behaving shitty. If you did all those, you either own one of the products crysis doesn't support(a list that can only be discovered by trail and error) or you encountered a pathing glitch where somebody got stuck a tiny piece of debris and immediatly devours your entire clock cycles by attempting to calculate an alternate path several billion times a second or something like that(happened to me, restarting game from lvl 1 (often) fixes it, don't use the autosave, it doesn't work).
Working rig(most things on medium): $350+
Good rig(everything exept killer apps on medium high): $800+
Built-to-last rig(everything exept crysis on max): $1100+
Going beyond $1500 is useless as the investment/return curve for hardware flattens extremly quickly.
Whatever you do, DO NOT BUY ALIENWARE. It's a $500 rig with a $1500 brand logo on it.
Running crysis on max is futile on even the best rigs in existance(think 4.2ghz OCed quad core, dual GeForce 280 XXX in SLI also OC and 8GB of 1066mhz RAM) because several of the max option are filled with memory leaks and it will grind itself to a halt no matter what eventualy without fail. Stop trying and hope somebody at crytek remembers to get rid of said memory leaks for crysis 2.