For security, there is no need to go beyond 2048 bits for RSA, which is already quite some overkill. 1024 bits are already at the threshold of the feasible. We go to 2048 instead of, say, 1400 bits, because we just love powers of 2. See this site for estimates of "strength" that various organizations have come up with. Summary: RSA-2048 is quite safe for the time being, and when it ceases to be safe, it will be due to technology that does not work like technology we know today.
In the not-near future, quantum computers, if they work at all, will break all RSA keys, regardless of their length. Classical computers, on the other hand, are likely to never be able to break 2048-bit RSA because of the involved energy consumption. That is, unless some half-mad mathematician discovers a killer algorithm for integer factorization, which is, as always, an unpredictable event.
Bigger keys are largely used to appease the paranoia and flatter the ego of people who are in position to decide about technical details but lack the actual competence to do so. Big keys imply obvious network and computational overhead (a 4096-bit key will produce signatures which are twice bigger than 2048-bit RSA signatures, and it will cost about eight times as much CPU), but also interoperability issues: 2048 bits work everywhere, 4096 bits are more restrictive, and bigger keys are not widely supported yet. Thus, there are real, factual, measurable disadvantages to big keys, while the security gain can be qualified as, at best, esoteric: bigger keys are stronger only in the face of unknown technology or science, about which we can only speculate wildly.