SHA-1, as a hash function, is known to be "slightly shaky". It is a 160-bit hash function (its output is a sequence of 160 bits); as such, it should offer 280 resistance to collisions, whereas it seems that its true resistance is closer to 261 or so.
However, OAEP does not ask much from its underlying hash function. It seems that collision resistance is not actually needed at all to ensure the security of the encryption system. See this article for details (it is a bit technical).
Bottom-line: we do not know of any attack that would work against RSA-OAEP by leveraging any weakness of SHA-1; we are not even sure whether such an attack can exist at all. In that sense, there is no known advantage, from a cryptographic point of view, in switching from SHA-1 to another hash function in the context of RSA-OAEP.
However, the current fashion is to shoot SHA-1 on sight and insist on switching to one of the SHA-2 functions (e.g. SHA-256 or SHA-512) systematically. Therefore, using SHA-256 is good for public relations, and will save you some time, because sticking to SHA-1 will require justifying yourself to a lot of people.
Note that SHA-256 has a larger output (256 bits), which imposes a lower limit on the size of the data that you will be able to encrypt. If using a 2048-bit RSA public key (256 bytes), the maximum message size with RSA-OAEP+SHA-1 will be 214 bytes (1712 bits), whereas it will be 190 bytes (1520 bits) for RSA-OAEP+SHA-256. If all you are encrypting are keys for symmetric encryption then this should not matter in practice.