Update 5/24: Google Maps added an "Avoid highways" checkbox to their route finding feature.
I'm a pretty big fan of all things Google and use several of their services and products. Google Maps, however, has a fairly serious drawback: Driving directions will always take you onto major highways and freeways -- where bicycles are prohibited -- if the highway is available. You cannot tell the route finder to avoid highways.
Back in the early days of online mapping software, this option was available but disappeared. It turns out the "No Highways" option has returned in at least a couple online mapping services.
MapQuest has a drop-down menu of "Advanced Options" where you can click "Avoid Highways." And avoid highways it does.
With Ask.com, you enter your start and end locations then click the "Walking" tab after the directions have appeared. The Walking option gives Ask a little more flexibility than MapQuest's "Avoid Highways" feature; Ask will route walkers the wrong way down one-way streets, for example.
In my tests, MapQuest's service seems a little more appropriate for cyclists. Ask.com seems to be very conservative on the roads it routes walkers on, taking you the very long way around, even for roads where sidewalks or good shoulders are available and pedestrians are permitted. MapQuest's "Avoid Highways" option consistently seems to provide a shorter route than Ask's "Walking" option.
Neither Ask nor MapQuest know about pedestrian or cyclist facilities -- pedestrian bridges and multiuse paths are not used by either mapping site. In the San Francisco Bay Area, some of these facilities make for valuable shortcuts that can take miles and headaches from my route.
I'm glad to see the map services recognize that their tools can be used for something besides driving directions. For the cyclist, I see these maps as a starting point. You'll still need knowledge of local conditions and compare the mapped route with what you can see on a local bicycling map.