How many Napoleonic medals are there?

Oh, a bunch of them. That's the short answer.

Perhaps the numbers involved in the references I've mentioned might help. Bramsen has a total of 2,330 entries in three small volumes. The Prince d'Essling's sale catalog had 3,053 coins and medals of which 2,392 were medals of some sort. Many of the lots were multiple coin or medal lots so it represents quite a few more than those numbers may indicate. Laskey described 141 medals and Edwards 564 for a 6 year period. Hennin described 927 different medals, coins and variants. Finally, British Historical Medals lists 609 different pieces dated between 1789 and 1815.

Most of the French and Italian pieces listed in d'Essling have Bramsen references. In all I would venture to guess at a number approaching 3,000 distinct pieces produced by all the major players in the period 1789 — 1815. Despite the references available to me I've managed to find a few over the years that I can't find in any of them.