I used to dump the grounds down the drain, I use a reusable gold filter. I also used to put egg shells down the drain and run the garbage disposal.
A costly plumbing visit has cured me of that habit. Apparently, the coffee grounds and any oil/grease and egg shells combine together to form the hardest substance known to man (sarcasm). Seriously, it was like cement in my outgoing pipe. It was quite a mess.
Now I tap out the grounds in the trash to get most of it, throw the eggs shells out too, and try to avoid putting a lot of grease down the drain as well.