I am looking for an asymmetric encryption algorithm other than RSA?
Almost all usages of asymmetric encryption is for key exchange (by encrypting a random string, which is then used as shared key in symmetric encryption algorithms). There are key exchange algorithms which are not asymmetric encryption algorithm, the most well-known and used being Diffie-Hellman (in a nutshell, DH is like an asymmetric encryption algorithm in which you do not get to choose what you encrypt -- the one who encrypts "discovers" the seemingly random data which has been encrypted once he has done it -- but that's good enough for key exchange).
ElGamal and Diffie-Hellman both have variants which use elliptic curves. Same principle, a bit more maths, better performance.
There are many other asymmetric encryption algorithms, e.g. McEliece and NTRUEncrypt, but they are less used for various reasons (too recent, too old, not studied enough to be declared secure, patented, too slow, public key is too big...).
Diffie–Hellman key exchange protocol DSS (Digital Signature Standard), which incorporates the Digital Signature Algorithm ElGamal Various elliptic curve techniques Various password-authenticated key agreement techniques Paillier cryptosystem RSA encryption algorithm (PKCS#1) Cramer–Shoup cryptosystem
Also features lesser-known algorithms, implementing software, and some insecure algorithms.