From: United States
It isn't common, but does happen. You can also end up with an enemy empire in the same system with you. Again rare, but does happen.
Good lord I had this happen to me in my last game, it was an incredible pain in the heiny, because the game decided that the system was always in the other guy's territory, preventing either of us from building anything beyond our homeworlds. To top it off, we were both races that hated each other, eventually I just said screw it, declared war, and wiped them out. Set me back a little, but not enough to prevent a win.
Other than the aggrevation of no building, it was kind of cool to have an "early warp" era war.