Someone shouldn't be able to remotely gain access to your machine unless you download some type of trojan.
If you're talking about the default Windows encryption, it is based on your login password, which is easily broken. If you're talking about third-party encryption, it would be inconvenient to encrypt and decrypt files every time you need them.
Software like TrueCrypt would work really well for providing near-invisible encryption, but I think it would be more aimed at protecting your data from someone with physical access to your computer.
Really, I would only encrypt data in the following situations:
1. You're in a multi-user environment and are worried about someone with access to your machine attempting to steal information.
2. Highly sensitive stuff, such as banking and budgeting information could be encrypted and decrypted only when needed.
3. If you really start to get paranoid, you could encrypt logs and caches. I, myself, and considering encrypting my browser cache.
But unless you're running servers on your machine, there should be nothing open to be compromised, and therefore no one should be able to remotely gain access to your machine without requiring you to download some sort of virus first, in which case a good anti-virus should catch it.