Based on a recent Slashdot post, here's a simple way to measure your Internet speed. The project is on GitHub at https://github.com/sivel/speedtest-cli, and to get the Python-based program, simply do this:
wget -O speedtest-cli https://raw.github.com/sivel/speedtest-cli/master/speedtest_cli.py
chmod +x speedtest-cli
Execute ./speedtest-cli --simple to get your results.
See ./speedtest-cli --help for details.
You can also try an HTML5 (no flash, no Java needed) Internet Speed test, http://speedof.me/
Hope this helps.