I think there is a bit more sense of doing something with no help using "by".

Although Peachey's post is down-voted, I think his comment does add to the discussion. I think "by ourselves" or " by myself" can often be replaced by "alone". If "we did it alone" wouldn't sound right, I'd keep it to "we did it ourselves". "we did it by ourselves" could mean that the group did what they did *while* being alone, without company. "we dit it ourselves" could just as well mean that there were a whole group of bystanders doing nothing (or other things) In general, I'd use "we did it ourselves", unless I wanted to draw attention to some feelings of loneliness during the activity. Loneliness makes more sense when a person is alone (all by himself). I think the cases are few where a group would feel lonely, left in the cold. The best example I can think of is a group of siblings who all miss their parents, but at the same time need to get something done around the house or so. The parents perhaps are perhaps very negligent. And even then, these siblings must form a group cohesive (and mature) enough to accomplish something while being by themselves. It's a pretty sad situation, if you ask me! "We were all by ourselves" is quite common, so the difference is really with "we did it". I think that there must have been some expectation of help, support or oversight, yet no one showed up.

Eric Carmen throws in his two cents: http://www.youtube.com/watch?v=D3j_fdSpkmE

No difference.