The actual number changes occasionally because new TLDs (top-level domains, also known as domain extensions) get launched on the internet from time to time. The current number of top-level domains can be found on this web page:
(disclosure: I work with the .BIBLE Registry)
What are the most valuable top level domains? If the winning amount of these auctions are an indicator of value, these are the top-level domains that the applicants believe to have the highest valuations:
Auction results are listed at ICANN… Only contention sets that resolved through Auction are included. That page will be periodically updated within seven (7) days after an Auction or update in status. Information about the Auction process, Auction proceeds or additional contention set status’ can be found on the Auctions page, Auction proceeds page or Contention Set Status page, respectively.
I confess that I don’t quite get how all of these top-level domains are worth millions or multiple hundreds of thousands. The ones that do make sense to me as having very high value are: .APP, .REALTY and .BUY. The others could sure have the potential of becoming valuable to the degree that the investors make their money back or get a profit, but that’ll take quite a bit of work.