I tend to buy every Call of Duty, that ended with this release though.
Why? Single player.

I would happily go back on a rainy day and fire up an older game and complete the campaign.

Nope

The only sport I'm interested in is football, and I really only buy the games when the Jets are having a really good season. So, no.

Nope, really don't see the point in them, I mostly play single player games outside of a few exceptions such as Overwatch/Rocket League and those games do not come out every year, there's just one and addon's/updates for them both are free since the games have come out.

I guess if I was interested in football I could see the logic behind buying one of those games, but even then, last years versions of the games are about 1/10th the price they were last year, is it really worth an additional 60e to make sure that player X is on team Y when you're playing these games?

I just buy them on a "Whenever I feel like it" basis. The yearly franchise I probably buy the most is Pokemon, but even then, not every time (usually skip the deluxe versions). As for the others, I usually buy the newest one when it's been a while since the last one. Might get Black Ops 4, since I haven't gotten a COD game since Advanced Warfare. Last year I went for NBA 2k18. On a side note: Wow, MyCareer loves to just bleed your wallet dry. If you plan to pick up an NBA 2k game, I'd suggest staying far away from that mode.

I can't say I've ever been bothered about the existence of these yearly franchises. Sometimes I want all-new experiences, but other times I just want to play the stuff I know I'll enjoy, just with a different coat of paint or new features here and there.

I used to buy then got bored of the yearly entries and their franchises, so I stopped

Yes if we count Assassin's Creed.

No. I don't think I've ever even bought a game out of an annualized franchised in it's relevant timeframe. I'm not interested in sports games or CoD and the only Assassins creed games I own I've bought several years after their initial release.
The clostest thing would be mainline Pokemon games, but since I tend to skip the remakes/enhanced versions at release and get them used later on, that's not really yearly either.

I do buy Pro Evolution Soccer (PES) every year since 2004. I also buy COD every year this generation. FIFA 18 every couple of years and eventually Battlefield whenever it is released.

Not really, it has a tendency to ring as watered down and corporate cookie-cutter to me, and I'm not really a fan of sports games unless they are more arcadey (The Bigs, Forza Horizon, Burnout, NFL/NFL Hitz, etc).

I was a regular buyer of the Guitar Hero and Tony Hawk series back in the day back when those were a thing, at least the first 4 or 5 games..

I've bought some of the COD games, but I pretty much limit it to Black Ops series, and the first couple MW games. I've played a bit of the AC franchise but mainly just 2 and 4 (because the pirate theme rules), though I might pick up Odyssey eventually as the Roman theme is pretty badass, being something of an Ancient Roman history buff.