In summary, if you did not receive your copy of Diablo 3 until Tuesday afternoon or evening, you did not miss out on a whole lot, given how utterly slammed the servers were (general rule of thumb: don’t really ever expect to play online games of this popularity immediately after release).
I was actually able to login without any problems (seemed to get in before Error 37 was an issue), but got stuck on the character screen in and endless timeout loop. Apparently though, the characters were created, given that my account was full of level 1 monks when I had logged in briefly the next morning to check my account. I have heard that a few folks were able to not only login immediately, but also create characters and play with little to no delay. All of those people are bastards lol. There were a couple more major server outages (servers were down effectively all of Tuesday evening and then for about one hour Wednesday evening immediately after I had arrived home from work lol…). Otherwise, I have been able to play lately without any real connection issues. I have been enjoying playing my monk; Currently level 21 in act II.