Recently I removed an old water heater stovepipe coming through my roof, because we moved our water heater. Right next to it was my plumbing vent pipe that I thought was associated with venting for the water heater, so I cut it off below the roof and patched my roof. So now my plumbing vent pipe terminates in my attic, in a little corner to be exact. How bad is this? I did it a week and a half ago and I never noticed any bad smells.
Bad. Not only are you introducing stink and moisture to your attic, but toxic and potentially explosive gases as well.
Decomposing waste materials in public and private sewer and septic systems create sewer gases. Methane is the largest single constituent of sewer gas, which includes an assortment of toxic and non-toxic gases, such as hydrogen sulfide, carbon dioxide, ammonia, nitrogen oxides, and sulfur dioxide. Improperly disposed gasoline and mineral spirits may also contribute to sewer gases.
Fix it now.
You should fix this (see isherwood's answer), but you don't necessarily need to extend it back out of the roof again, assuming that you have at least one vent to the outside somewhere else in the system.
You could instead cap it with an internal drainage vent (also known as an air admittance valve). This lets air in (necessary for good drainage) without letting sewer gases out.
It's probably a vent not a drain. Yes, it allows moisture and odors into you attic and it needs to be extended at least 12" above the adjacent roof. If you cap it, the fixture it comes from will not drain properly. If it's a drain, then add a vent through the roof too.