UPDATE (May 2022): From @AbdullahTahan:
Now google has this feature but it’s paid and costs 0.01$ per request check this https://developers.google.com/maps/documentation/distance-matrix/distance-matrix#distance-matrix-advanced
UPDATE (March 2016): A lot has happened since this answer was written in 2011, but the core points appear to hold up: You won’t find raw traffic data in free API services (at least not for the U.S., and probably not most other places). But if you don’t mind paying a bit and/or if you just need things like “travel time for a specific route taking traffic into consideration” you have options. @Anto’s answer, for example, points to Google’s Maps For Work as a paid API service that allows you to get travel times taking traffic into consideration.
ORIGINAL ANSWER: There is no way (or at least no reasonably easy and convenient way) to get the raw traffic data from Google Maps Javascript API v3. Even if you could do it, doing so is likely to violate some clause in the Terms Of Service for Google Maps. You would have to get this information from another service. I doubt there is a free service that provides this information at the current time, but I would love it if someone proved me wrong on that.
As @crdzoba points out, Bing Maps API exposes some traffic data. Perhaps that can fill your needs. It’s not clear from the documentation how much traffic data that exposes as it’s only data about “incidents”. Slow traffic due to construction would be in there, but it’s not obvious to me whether slow traffic due simply to volume would be.