I think you could probably add tennis to that list. Everyone goes a bit tennis mad during Wimbledon, but a fair few people follow the sport year-round as well. Popularity certainly goes up when a Brit is doing well. You might also want to have a look at Formula 1. Not sure if you could call it a sport, but it is very popular over here. Darts, as well, is gaining popularity (especially since Phill Taylor came third in Sports Personality of the Year).
And also, we have pool over here too. The only difference I know is that snooker has lots of different coloured balls whereas pool only has two colours. I think you have to pot the balls in a certain order in snooker, but other than that, I know nothing about it. Pool is mostly played in pubs. That's where I play it.
With Rugby, there's a sort of north/south divide as to who plays Union and who plays League. Or rather a Yorkshire/rest of the country divide. In the south, Union is more popular, and I think it's more widely followed. The Six Nations competiton that's just been is Union, as well as the World Cup games shown on the TV. Not sure if Rugby League has a World Cup.
Wonderful avvie by psijupiter. Totally brilliant and amazing banner by Julia/the opaleye!