Satellites are purely defensive weaponry. They are the cheapest of all the ship types to both build and maintain. Further, they use no fuel, only minerals. The major drawback to satellites is that they cannot move, which limits the planets that can be defended using them.
Satellites are a favorite of many players, though I prefer to use them only when absolutely necessary. Because they are purely defensive in nature, their role is generally limited — and I prefer to always be on the attack anyway. I therefore tend to use them only on periferal planets, to leave a token defense there to discourage free exploration in that area. To be truely effective, satellite usage must be limited to builders at the head of a bottle-neck. If the opposition can simply explore and go around your defenses they will do so, knowing your satellites can't move to stop them.
If you are able to keep the enemy's fleets at bay with satellites, you must still watch out for cloakers. If your opponent can see planets behind your satellites he can slip the cloaker through and nuke them. Desite what others have claimed, satellites cannot detect cloaked ships traveling through their system. Some players maintain that there is a dip in the satellites' BR when a cloaker passes through, but objective tests of this theory have never shown it to be true.
The Sat Wall
This being said, satellites are supurb in carrying out the role they were designed for. If you can create a builder planet that the opposition does have to go through, satellites can keep them out more effectively than any other ship. Since satellites are so cheap, you can often build more of them than an attacker can sent at you, even if his economy is significantly higher. There are few ways to get through a large sat wall, but most of them take time. Add a mine to the defensives and you force the enemy to spend that much more resources in building a mine sweeper to accompany their fleet.
Chopping through the sat wall can best be done either by a cloaker fleet catching you overbuilding or by someone with a stargate or a builder right next to the sat wall continuously building and throwing enough high BR ships at the wall that your resources must go to repairing the surviving satellitess rather than building new ones.
If you are reasonaby even in economy then you can turn this assault to your advantage. Such a constant attack will drain the opponent's tech development much faster than it will yours, and this may allow you to reach the next BR level well before your enemy. When this happens you can dismantle your satellites and build an attack fleet with the BR advantage.
The one downside to keeping a large sat wall is that the other player may decide to dismantle everything and just wait you out. Satellites may not cost much in resources, but they're not free. Since you can't move your satellites, your opponent knows you can't attack him, so he can sit back and build BR faster than you. This is one reason it's wise to include at least a few attack ships along with your satellitess (even if they're just BR-1, the enemy will still have to respect them and build at full BR to defend, thus lowering his tech development.)