Bad to run no tailpipes?

It wont break anything. You will just have more fumes and noise but I'm sure you already know that.

just put some turndowns on the end of the mufflers

You should try to run your exhaust out the back or sides (in front of the tires of course) if this is your DD. If you're just using it for racing then that is another story.

Carbon monoxide is a by-product of the combustion process and it will accumulate under the car. You will find yourself breathing/smelling it. I makes me feel like *****, personally. I get enough headaches from other stuff, I don't need more.

Just my 2 centavos.

If you go the side-exit route (it's really not that hard or expensive), and you're using muffs with a center or offset outlet (instead of same-side inlet/outlet muffs), just buy two U-turn (180*) mandrel-bent pipes from Summit or Jeg's, two 90* elbows, two universal clamp-on hangers, and some heat shielding for the passenger-side pipe (it'll pass right under the fuel lines, best to insulate those somehow). It's wiser to go with side-exits than dumps, IMHO, because it'll keep you legal in most states and you won't have the carbon monoxide issue to deal with that you'll get with dumps.

As far as harming anything ... well, about the worst you'll have to deal with if you're running without tailpipes or turndowns is that everything under your car from the axles back is going to be covered in soot if you're running even slightly rich, especially if you're running without cats. The original owner of my notch had this setup on it for years, and I get thick, nasty crappy smears of PITA-to-clean-off carbon on me every time I so much as brush something against the underbody.