Are solder fumes bad for me?
Solder fumes aren't very good for you. Some people can become sensitized to flux fumes, especially from the older rosin flux used in cored solder, and get breathing problems:

Controlling health risks from rosin (colophony) based solder fluxes

The no-clean flux isn't as bad.

I once felt quite ill after assembling about 30 boards that I had to do myself as my distributor wanted them very quickly.

Breathing out whilst you are soldering each joint helps a lot, if you don't have fume extraction.