It's a broad question, but here's my opinion:
Performance-wise, the hit is not that big those days. It's block level encryption and everything did pretty fast. Unless it's some heavy load you should not feel the hit.
- Dev/Build server: No need.
- Demo Server: No Need.
- Production Server: Only if you are dealing with crypto stuff/certificates/etc.
- Definitively yes.
The *No Need*s are because they are probably inside your network, firewalled, protected inside a secure place. The Maybe is because they may be in the same position as the *No Need*s. Laptops are a no brainers. They can be stolen, lost, kidnapped, exposed and so on, you definitively want that data encrypted.
Also, remember to encrypt your swap. If you usually hibernate or suspend your computer there's a lot of important data that can sit on memory/swap that can be salvaged if it's not encrypted.