Cosmic Encounter. This game is often considered to be a cult classic as can be witnessed by the fact that it keeps getting re-released (in fact, my copy is this one: Cosmic Encounter).
In Cosmic Encounter, each person takes on an Alien Race from a specific galaxy (color), and the object of the game is to explore the galaxy and wind up with 5 colonies outside of your home galaxy. This exploration can be either peaceful or violent, and can wind up as intergalactic struggles as each player in the encounter has the option of asking for allies.
Starting with the pros of Cosmic Encounter: for the people that enjoy the game, there will be a decent amount of replayability because there are many more races than player allowed in a given game (it is up to 4 player), each of which has different abilities and so it can be replayed several times with different aliens. Secondly, the negotiation of the game is crucial, and for people that enjoy negotiating games this can be quite fun. In fact, most encounters are heavily swayed by whether allies join you in your attack (or defense), and in what numbers they arrive. Thirdly, encounters are decided by 1) sheer numbers but also 2) which encounter card is picked. If both players pick a negotiation card, then they are able to peacefully decide on how to end the encounter and leave the allies out in the cold. (Of course if only one person decides to negotiate and the other wants to attack.... well.... that's not so good for the pacifist.)
The biggest problem with Cosmic Encounter is the lack of depth to the game. Each turn you make an encounter (you don't even get to pick which galaxy - it is randomized each turn) and if the encounter is successful, then you are able to make another encounter. Because of this, there just doesn't seem to be that much going on in the game.
Another problem is that the Alien Race abilities don't seem to be especially balanced. For example, one of the aliens in the game is able to heal other races' (read "not their own") ships when they are blown up, whereas another race is able to swap cards when an encounter occurs (but at least before they're revealed).
Overall, I think Cosmic Encounter is very hard for me to give a firm rating on. I will mark it as a 7.0/10, but I have debated about numbers anywhere from 6 to 8. If it is played with the right people, I think it could be enjoyable, but if played with the wrong people it could be miserable. Let's hope that if you play it, you have the right friends!