never enough pedals!
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Who's in a bunker?
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And the children first
And the children
Anything you put in the signal path is going to affect the tone, but probably not significantly. Too many pedals will degrade the signal, and you will need a signal booster somewhere in the chain in order to bring it back up to full strength. More and more high-quality pedals have true bypass, so the tone-diminishing properties have been reduced. You can definitely overdo it with pedals, though. If your pedal board becomes too heavy to lift with one hand, you've probably got a problem.

If you use a lot of pedals, you can get a pedal controller to set up schemes where you use only certain pedals at one time and the others are removed from the signal chain. Carl Martin makes a very good one that lest you arrange for eight different schemes for your pedals: