According to AW Stats (and Analog) people are searching using various 18 digit numbers as keywords and thereby finding my sites. Perhaps it is a session number from a search engine? The only search engines listed in the logs are Google, Yahoo, and MSN - and they don't seem to use session IDs.
Coincidentally, on sites that have these numbers in the log files, positions have tanked when these numbers started appearing. May or may not be related.