Web throughput measurements include Internet delay and so are not absolute or highly repeatable, but they can be useful to compare tests performed within a short time span, through the same point of Internet access. For best results, repeat many times and average results, discarding anomalies. Some free "speed test" Web sites include BandwidthPlace, CNET, McAfee, and Speed-Test.net.
FTP throughput measurements can be affected by file content and compress-ability, so you might want to use a large file that's already been compressed (zipped). Once again, repeat your file transfer several times and average results, which can be seen easily in most FTP client programs. The file should be large enough so that results are fairly consistent (repeatable) under the same conditions.
If you want something more rigorous but free, then you might try an open source or freely-available performance test program. Examples include NetPerf (from Atheros, zipfile) or Qcheck (from Ixia / NetIQ).