How many chess variant are there? (Apparently a lot.) If possible could you include the popularity of each variant and its major event. For example, I know that there's a US bughouse chess championship. The list doesn't have to be comprehensive.
To simply name a few of the variants here would need a huge amount of space, because there are many. However, you have a list of variations in the Wikipedia entry:
This entry is not comprehensive, and a few variations that cannot be found there appear in the webpage:
These sites do not come with popularity rankings, and the same way chess itself probably does not have a "major" event (one could consider the World Chess Championship to be it, but as only two players play and the number of games and funds has been so drastically reduced, I'm not sure anymore), probably there is not a single "major" event for these variants too. However, to a certain extent, the length of the Wikipedia article on a certain variation can measure its popularity, so I suggest you take a look at the Wikipedia category:
The Chess Variant Pages actually does have a couple of rankings (at least one is new since Pablo's answer):