I can't say I do too much on my own, not because I don't want to but because I've never had the opportunity.
I have done my own oil changes and quite enjoy doing them, but Mike is always around the garage so he can help with little bits and pieces. I am still a bit afraid of reefing on the wrench too hard. As if the bike is going to fall over, right?!?
Also, I have bled my brakes but for anyone that has done that it is not really a one person job, so admittedly Mike and I do this together.
Oh and since my current bike doesn't have a center stand, even lubing the chain takes two people.
The only thing that Mike has done on his own to my bike (if I remember right) was the recent coolant change, and I think that was because the coolant reservoir was tucked way under the winking and we didn't want to take off the plastic and it was just easier for him to rig it all up without a second pair of hands in the way.
Other than that I haven't had to do much else. But I agree with what a few of you said above, leave it to the professionals when it's something really important.
At least I can say that I am not afraid to try, and not afraid to get my hands dirty. GoJoe is your friend!