I've just recently began colonizing planets, and I recently stumbled upon two planets with 450+ fields each. I've been wondering though, should I specialize my planets and have one for research, one for ship construction, etc. Or is it more effective to spread it out and have roughly the same amount of research labs and shipyards at each planet?

You may build your empire in any manner you see fit. However, experience has shown that when you specialize a planet to perform one function you either become a farm for the rest of the Universe or you spend way too much time and fleet slots supporting it.

I would highly recommend that you do an "even build" plan with a few of your bigger sized planets acting as a "primary"- ones that are heavily defended or where you concentrate greater effort.

Ok, thanks for the help. I've got two more questions now though.

1) If you build ships at Planet A, and you send them to support Planet B, will those 2 fleets combine, or will they stay separate. (By combine I mean they can all be used in one attack, or moved in one group) If they don't combine, does the support count as one of your fleet slots.

2) What does the terraformer do? I looked around and I couldn't find it, and it's been bothering me for a bit.

A fleet deployed to Planet B merges with the fleet parked there and they become one combined fleet.

A Terraformer is a Research tool that allows you to expand the number of fields on a planet. In other words, it gives you more building room. However, they are very expensive and give you little extra room so shop for a bigger planet instead.

NOTE: Terraformers will NOT add fields to a moon's size.

In my opinion the only real reason to terraform a planet is if you get a moon on a planet that isn't very large to begin with, and want to expand it.