The bins are first come, first served.

Was on a CAL 737 last night in the exit row. The entire bin, on both sides, over those seats is taken up with the life rafts. Obviously, you put your bags wherever you can find room.

Actually, I haven't found it to be a problem these past few months. Even on a full flight (domestic, narrowbody) there's usually plenty of extra room in the bins due to the increased amount of bag checking with the 3-1-1 rules. I'm usually able to move my underseat bag to the overhead at the end of boarding.