Due to being hybrids we match up well with any other class, it's just knowing how to synergize. It also depends on what you actually want to do.
For example I leveled my first Shammy with a RL friend who was leveling a hunter, it was an awesome combination we could take down large groups with ease (even groups of elites on occasion) with the pet tanking and me alternating between dps and healing (Enh specced).
The time it really rocked was in world PvP encounters though, seriously, try getting away from a hunter shammy combo. Aspect of the cheetah and ghost wolf, as soon as he was in range he'd pop a concussion shot then I'd catch up, frost shock and we'd proceed to tear them apart.
This same friend an I are currently leveling another combo together, this time he's the shammy and I'm a prot spec Pally (now 69 and 68 respectively). Yet another awesome combo (dual hybrid combos are always good though). In this case PvP is not so open shut but PvE grinding is just insane, massive pulls, AoE tanking with him alternating between DPS and throwing me the occasional heal. Totems + Blessings = WIN.
This combo is also very effective for instances, I tank (obviously) and even though he is enhancement he's a great player and tbh a better healer than a lot of specced healers I have played with recently. Of course if we do get another healer then he can break out the DPS :-).
My basic advice, team up with a mage/lock/hunter if it's a PvP server, or a war/druid/pally if it's a PvE server.