You have the power of immortality

(From the official description at Cosmic Encounter Online) - You have the power of immortality. Whenever you are about to lose any of your ships to the Warp, they relocate to your colonies.

What does this mean?  It means that the sweet smell of rotting flesh is in the air.  What's great about Zombie is that you can stink it up as much as you want (yes, pun intended)  in an encounter, and you don't lose ships to the warp.  You can participate in any encounter (whether as main player or ally) without worrying about bad play on someone's part resulting in a trip to the warp for you.  Zombie is one of the original aliens in the Cosmic Encounter board game, and it is also one of the aliens that free players are allowed to use for Cosmic Encounter Online.  Thus, pretty much everyone has or will play as Zombie at some point.

Example:  You are the defensive player in an encounter.  You play a 10 and the offensive player plays the 40.  You lose, but your ships don't go to the warp.  Instead, they are evenly distributed to any of your home planets where you still have colonies.

After Zombie's power is activated, Zombie can be zapped.  In such a case, Zombie's ships go to the warp, just like those of any other player.  If Zombie is in an encounter where it loses to Void and Zombie is zapped, Zombie's ships are permanently lost.

Bring 4 ships to any encounter where you are the offensive player (unless you're playing against Anti-matter).

Take advantage of opportunities where you are invited as an offensive or defensive ally.  Bring 4 ships when you are an ally.  If your side loses, your ships are returned to your home planets.  If your side wins, you get whatever rewards are accorded to your side (i.e. a base is you are an offensive ally; pods if you are a defensive ally).

Be wary of acting as offensive ally to a power alien such as Virus.  You might gain a base but lose the game if another alien can use you to acquire enough bases.

Consider how you will use the pods in your hand, and how you will get more.  Unlike other players, you get no pods if you play a negotiate ("N") pod as a main player in an encounter.  Thus, the only way to get more pods short of running out of encounter pods is when you are a defensive ally..

When you are invited to act as offensive or defensive ally, consider who is more likely to win.   Since you may need to find ways to get pods, it may at times be advantageous to ally with the defensive player.

While it doesn't necessarily make you the most popular player, you can use the Zombie power to send other players to the warp.  (This maneuver is occasionally referred to as a "Syz," so named after one of CEO's best players who regularly uses this tactic to his advantage.)  As an offensive or defensive player, you can invite allies and then purposely lose.  Your allies ships will go to the warp; yours will not.  This is an especially useful trick in games with Virus and other aliens that rely on their ships for strength.

If you get the plague artifact, it can be advantageous to use it on yourself when you're trying to get rid of poor pods in your hand.

IN A GAME WITH MACHINE,  you may want to ally with defensive player EVERY time when Machine is the offensive player.  If Machine takes many offensive turns, and the defensive player wins a number of those turns, you will quickly accumulate a large number of pods.. 

Zombie is not a particularly powerful alien.  Even the best players struggle to win with Zombie.

Remember that Zombie's power is, in some ways, basically the power to ally without fear.  Thus, you may want to avoid inviting Zombie as an ally, since you have something to lose and Zombie does not.

Zombie is the bane of Void, Machine, and Warpish.  ("Bane" is a fun word that we so seldom get to use.)  Zombie negates the power of Void and Warpish, and can make Machine's life difficult by always acting as a defensive ally.  All of these aliens benefit by zapping Zombie, and all of these aliens benefit by depriving Zombie of three home planets and thus ridding Zombie of its power.