Whenever your bitcoin client creates a new address, it randomly creates a public/private keypair of one of the 2^160 possible addresses.
If (and it's a HUGE if, with a VERY low probability, but it's not ZERO) you create a public/private keypair that someone else has already created, you'll have access to the coins in that address in the block chain.
Elsewhere in the forum someone was working on a program that would generate approximately 80,000 bitcoin addresses per second.
At that rate you can create 80,000 * 31536000 (seconds/year) = 2,522,880,000,000 (2.5 Trillion) addresses a year.
However, you'd have to run that for 5.7929891129617856×10^35 years, to exhaust all of the address space.
And of course, you'd have to have a client that could handle that many addresses, which I doubt the default client can do. So, you'd have to come up with a way to check them all in the block chain to see if they are valid, which would slow down your rate.
It's a big number. So, the odds of two people colliding with the same address are astronomically tiny.
You'd be better off using vanity ID creation code to try to create a specific address, at least then if/when you found it, you'd know it.