It's not possible though. Well ok it is if you are really really really hate EA. But they own some of the best IP's out there.
Mass effect as mentioned is a great example of that. The first game (apart from the PS3 version which was released at a much later date) had nothing to do with EA. The 2nd and 3rd (which arguably are not as good as the first in my opinion) are published by EA. So after playing the first, really enjoyed the story the lore etc... it is natural to want to play the sequels. Regardless of which publisher er publishes it.
Fifa is also a good example. There is one other competitor PES and well... (again in my opinion) PES is awful. So if you want to play a football game you don't have much choice.
Because of this, the people who just don't purchase EA titles are the extreme minority and well just end up missing on the good games EA do release. Mirror's edge for instance.