I only pay attention to average speeds for the rides I do during a triathlon. Other times, I'm either riding for fun or doing something specific where average speed is not important. I do keep track of it though (distance travelled / elapsed time including stopped time), so here you go:

My average speed to work varies signifiantly by weather/bike/tires etc. I have 3 ways to work...two of them are 5 miles, the other 8 one way. 5-mile 1 average is typically 12mph or so in good weather conditions on my cyclocross bike with slicks (lots of stopping and have to cross a major hwy with no stop in cross traffic). 5-mile 2 I average about 11, but its newly opened so I've only done it in snow/cold conditions on my hybrid. That 11 mph is into the prevailing wind. Coming home the other day my overall avg ended up as 17 mph. Gotta love a 20 mph tailwind the whole way home. The 8 mile route I've done in both poor and fabulous conditions. Typically in good weather on my cross bike with 700-28s I avg about 16 mph or so with an all time high of 19.8 mph when I hit all the lights without having to slow down, no wind 67 deg F. That was my sprint workout for the day. In cold/snowy weather on my hybrid I average about 11-12 mph.

Now the measure that really matters: how long does it take you from when you hop on your bike to when you start working? For me this is almost always 1 hr. If I go slower I tend to be faster with locking up the bike and showering...If I go faster I lose the time gained recovering from the workout and walking slower, pausing longer etc after locking up the bike. In the end, all that matters is that if I need to be at work by 7:30, I need to straddle the bike at 6:30.