There's a useful device which is a muffin fan in a shroud, with a charcoal filter on the back. Put this next to your soldering station and it sucks up the fumes.
Lead-free solder is the way to go now. I know, it's a pain because of the higher melting point, but it's the future. Also, you can get the kind with a little silver in it to bring the melting point down. Unless you're running a large production shop, the slightly higher cost won't matter. The student electronics labs at Stanford now have a No Pb sign - no leaded solder allowed.
Please don't breathe solder fumes.
That picture of everyone hunched over their PCB boards while soldering makes me cringe.
Use some form of protection via a fume extractor or face mask and when possible solder in a well-ventilated area.
I've met people who've completely destroyed their lungs and ended up with nasty lung cancer after years of day-to-day solder fume exposure.