tzenes & Shaun really made the point clear, but I wanted to add a couple more benefits to spreading that I think help support their answers:
Siege tanks almost always get focus-fired by the opponent. The risk for your opponent in focus-firing is that his units spend time traveling to the target instead of attacking the nearest. This increases your benefit of putting physical distance between tanks. The time the enemy spends traveling is usually more than the time the enemy is attacking.
If you group 3 siege tanks, it will be obvious to the enemy how many you have and where they are, and he can take an appropriate decision. By spreading them, he has no idea how many you have, and it's much harder for him to evaluate positioning. Imagine the image below represents the area your tanks can do damage. In the clumped example, your enemy will know exactly where to go to avoid damage:
damage area http://bit.ly/g16c2WKind of obvious, but you cover more ground, preventing counter-attacks and limiting the enemy's positioning options. On Xel'Naga Caverns, you can control the entire center by spreading your tanks. Clumping would leave you more vulnerable to counter-attack.
Leap-frog behavior in a siege line. Usually through a battle, there is a geographic push and pull. The center of the battle will move back and forth. If the battle goes out of range of your tanks, they become useless. If the tanks are clumped, you would need to move them ALL in order to change the center of battle, which means no siege tanks at all during the relocation. If they are spread out, you can leap-frog them around which:
- Gives you more options regarding positioning
- Decreases risk. You will only be moving 1-2 tanks at a time. If you make a bad decision with 1 tank, it's much better than making a bad decision with all of them.
- Maybe it's easier. For some reason to me it is just easier to move 1 tank rather than move all of them. You can even queue up the entire relocation - unsiege, shift+move, shift+siege. Yea I realize you can do that just as easily with many tanks, but for some reason to me it's easier with only 1. Maybe it's that they are big units whose position is so important that queuing up a move command is dangerous, or maybe it's because the impact on the "siege cloud" is small so the decreased risk makes it easier to do. YMMV.