Quick way to check my broadband speed
www.speedtest.net
Or google broadband speed test.
rough idea may be ascertained to what your modem thinks your speed is if you poke around the interface. Some tell you the connected speed. Speed tests are inaccurate as it depends on what you're hopping through, but give a rough idea.
EDIT - To have a more complete answer, as others pointed out, there are other sites that will test your speed. I've used DSLReports for information before and they seem reliable as well. I can't speak to other sites, though.
I would point out that all these sites have other variables involved in measuring your speed and can only give an idea. Don't place complete faith in the results of any place...get averages from multiple sources and treat them as rough estimates, and go from there.
Speedtest is crap. Seriously. They consistently overrate my connection speed by 15Mbps.
As near as I can tell, many ISPs (I have Cox Cable internet) use modems that do compression. Speedtest.net appears to use test-data that is highly repetitive.
The end result is they often overestimate your connection's speed by as much as 100%!
DSLreports and TestMy.net both use largely incompressible data, and seem far more accurate. I still get a fair bit of variance between their results (and variance between the different types of test), but they're in a far more believable regime than speedtest.net.
(Copied from my answer here.)