If you have a run-in with any repulsive race early on in the game (especially the Silicoid), defeat them as fast as possible, otherwise their fleet will be too much for you. It helps to customize your race with the following: Cybernetic (to repair your ships during combat, like the Meklar; it hurts early in the game by taking 1 production and 1 food for every 2 colonists (rounded up) instead of 1 food/colonist, but is convenient and saves you from having to add the "Automated Repair Unit" special to your ships), Telepathic (this serves a 4-fold purpose:

1) it prevents other Telepathic races (i.e. the Elarian, and other races who customize themselves as telepathic when on Hard or Impossible mode) from taking your colonies over without Troop Ships.
2) it adds to your Spying bonuses (+15 to defensive i believe)
3) it allows you to Mind Control your opponents' planets so their colonists are immediately assimilated and you don't have to worry about building/buying an Alien Control Center.
4) it allows you INSTANTANEOUS control of any ship you capture from an enemy (although if they capture it back and you take it back again, you lose control of the ship for that combat).

If you cannot defeat their fleet, go directly for the kill *IF* you can; take over the planets so you have a jump-off point in case another fleet arrives and decides to blow out it's own race on that planet. Once you take out enough planets, the main fleet will deminish in size due to not enough resouces to command them.

Also another way to easily defeat your opponents is to have a colony at a wormhole. if your opponent has a colony at the other end of the wormhole AND cannot reach you at any other colony, you are safe from attack until your opponent acquires fuel cells that can reach you. For some reason, your opponents will not use the wormholes to their advantage, unless they are already sitting on a colony with a wormhole and have access to one of your colonies which is the only one they can reach (which is usually one you just took over).