According to https://en.bitcoin.it/wiki/Target the target is a 256-bit number. As the total hash-rate of the Bitcoin network rises, this number decreases to increase the difficulty. How much hash-rate (in terms of GHash/s) would cause the target to reach the minimum value? will the target ever get to 0? Does that mean it will be impossible to find a new block? (the minimum of a SHA256 hash is 0 which is not less than 0)
The hardest possible target is all zeros plus a one (
0000000...1). If such a block were ever mined (which is extremely unlikely: on average you'd need 2^255 hashes per 10 minutes, which is 9.6e73 hashes per second), it would definitely crash the network : there can only be one hash at that difficulty, which means that there can only be one block mined at that difficulty.
Of course, if the target is zero, no block can be mined at all.