I am rather late to the discussion (my account seems to have disappeared too so I get to be a new user again :( but as a commuter/recreational cyclist who puts at least 100 miles down a week in the city, I have some thoughts. I am not trying to tell any of you to ride beyond your comfort level or to compromise your safety but I do hope to change your perceptions of "safe riding"
While I think the legal disposition of "Bikes on Sidewalks" has been adequately cited above, I would like to talk a little about WHY it's a bad idea for cyclists to ride on the sidewalk. I will try to avoid sounding like I am lecturing but these are hard-won personal observations along with data points (Specifically, Driver-Action/Reaction times) provided by the NHTSA.
1. Visibility. This is both regarding what you as a cyclist can see and perhaps more germane to the conversation, what motorists can see of you. Sidewalks often have obstructed fields of view due to light/power poles, trees, pedestrians, or currently, oversized-political signs (different discussion I know :) If they can't see you, you have a problem. Especially with vehicles traveling in the SAME DIRECTION (Right-Hand Turns) as you probably can't see them either.
2. Driver habits. When learning to drive, we as motorists are taught to scan pedestrian crossings and the general area around them. That general area for a CAUTIOUS driver is typically a distance no greater than about 20 to 35 ft. of sidewalk in either direction. We establish these distances because we become conditioned to seeing very few moving objects on the sidewalk going more than 7 miles-an-hour(very-brisk walking pace)or 10.3 ft per second. In the typical 2 to 2-and-a-half seconds it takes a motorist to initiate, execute, and clear a maneuver, even a fast walking pedestrian is only going to cover around 25 ft.
Above, a poster mentioned riding at around 10 miles per hour on the sidewalk on her bicycle as being a "safe" speed. Let's apply the formula again. 10 MPH = 14.7 FPS x 2.5 sec = 36 3/4 ft. Put another way, that motorist and cyclist are potentially attempting to occupy the same space at the same time.
3. Control. This really addresses two issues. One being physical control, the other being an attitude about how we share the roads. In terms of physical control, I don't really have to go into detail beyond saying that a cyclist going speed X will virtually ALWAYS require more distance to stop than a Jogger/Runner/Skilled Roller-blader going the same speed. It's just physics. Hence, if after reading point 2 you said "Well, what about runners/joggers?" I hope that addresses your concerns.
The more substantial issue regarding control is part of a defensive rider/drivers attitude. The mantra for me goes something like this. "I can control what I do, I can't control what you do". This could range anywhere from finding alternate routes through troublesome areas or avoiding riding certain sections of road at certain times(Like taking side streets, the MORPC map is pretty good for this) to making sure my bicycle is in good repair. I can also commit to being clear with my non-verbal signals to motorists and other cyclists about my intentions and when a motorist DOES acknowledge my presence by waiting to make that turn or pass or whatever, I smile, I wave or nod, and I engender good will for myself and other cyclists. Or at least I wanna' believe I do ;)
4. Danger to pedestrians. It's not their job to move for you. You're on their turf and need to keep that in mind. Especially if they have a dog or are pushing a stroller or god forbid, both a dog and a stroller. (Looking at you Short North Moms) Now, if you are unfortunate enough to have a collision with a pedestrian on the sidewalk, even if they jumped in front of you, YOU will be the one to get cited should the cops get involved. If they are injured, you could be looking at a civil suit to boot.
Okay, I think I have made my case about why sidewalk riding is dangerous. Do I expect you "No lights, no helmet, dark-clothed people" to listen? Not really but you are an accident waiting to happen anyway. To the folks who are trying to ride safely, if you still insist on riding on the sidewalk, please commit to coming to a near full stop at EVERY intersection you cross to check for traffic including other cyclists. Be safe and ride hard!