How many products can Drupal Commerce handle? Are there any limitations on how many products Drupal Commerce can handle?
Interesting question. The major limiting factor for any Drupal Installation is server resources. If you have unlimited budget, it's safe to say you can have unlimited everything. There are upper limits to the architecture, but it's probably a limitation of database structure, that can be avoided by using a different kind of database.

For Drupal Commerce, the biggest limiting factor in Drupal 7 is usually not number of products (one of the companies I've worked with in the past did some tests with millions of products, and it worked just fine), but it is number and frequency of orders. A really busy ecommerce site is dealing with thousands of orders per hour. 

I've personally seen tuned Commerce installations that can handle that kind of traffic at peak times and not crash. It takes a very dedicated team to scale any resource like Drupal Commerce to such heights.