chsnyder writes that the data is limited to 936 bits in his implementation.
Actually, it has nothing to do with RSA being CPU intensive, RAM or anything of the sort.
Basically when you encrypt something using an RSA key (whether public or private), the encrypted value must be smaller than the key (due to the maths used to do the actual encryption). So if you have a 1024-bit key, in theory you could encrypt any 1023-bit value (or a 1024-bit value smaller than the key) with that key.
However, the PKCS#1 standard, which OpenSSL uses, specifies a padding scheme (so you can encrypt smaller quantities without losing security), and that padding scheme takes a minimum of 11 bytes (it will be longer if the value you're encrypting is smaller). So the highest number of bits you can encrypt with a 1024-bit key is 936 bits because of this (unless you disable the padding by adding the OPENSSL_NO_PADDING flag, in which case you can go up to 1023-1024 bits). With a 2048-bit key it's 1960 bits instead.
But as chsnyder correctly wrote, the normal application of a public key encryption algorithm is to store a key or a hash of the data you want to respectively encrypt or sign. A hash is typically 128-256 bits (the PHP sha1() function returns a 160 bit hash). And an AES key is 128 to 256 bits. So either of those will comfortably fit inside a single RSA encryption.
