Is it possible that a virus could be included in the block chain or even spread out to computers as miners are trying to mine? I'm new to BitCoin and curious about a lot of things about it, and about the mining network. So is it safe for everyone to mine and not get their PC or other machines get hit by a virus if it goes along the transfer of information? How safe are we from this scenario as users?
Ideally it is safe, the data transferred in bitcoin protocol is never meant to be executed. However:


The transactions themself are programs. While they are limited and cannot directly affect your computer, they can be just very computationally expensive, DoSing your PC. This attack is impossible now and in foreseeable future, since any non-standard transaction will not be evaluated.
Not virus, but it is possible to include arbitrary text messages inside blockchain. Therefore, one can include something that is illegal in some jurisdiction, potentially making bitcoin illegal as well, since blockchain can not be retroactively redacted. However, it is dubious whether such trick will actually work (1, 2). But there was some commotion about including catholic prayers in block headers.
There might be some bugs in bitcoin software (be it client or miner), just like in any other software. For example, it is possible to crash a computer by sending specially formed ping or execute code by sending packets to a closed network port. This applies to all software and is not bitcoin-specific.