The Internet currently has 1,532 Top Level Domains as of February 20, 2019. This number may change from time to time, whenever new ones are delegated or old ones get retired. 
There are 5 groups of top-level domains:
- Country Code Top Level Domains (ccTLD)
- Generic Top Level Domains (gTLD)
- Sponsored Top Level Domains (sTLD)
- Unsponsored Top Level Domains (uTLD)
- Infrastructure Top Level Domain (arpa)
In most cases, the top two groups are what most people are going to register. Generic TLDs like .com, .net, org, .blog etc are some of the more popular with .com as the most sort after.
Country based TLDs may require certain credentials specific to that country’s rules to register. For example, to register a .com.au you must have an Australia Business Number (ABN).
Having said that, my own site has a .me TLD which is now considered both a ccTLD and a gTLD. As of July 2008, .me became recognized as a legitimate Generic Top Level Domain. Originally, .me was in fact a Country Code Top Level Domain reserved for Montenegro in South Eastern Europe.