I was sceptical but got a great deal on one last year (£30 for a digital 6.1L one) and we use it almost every day.
My kids are 20 and 16 and neither of them like the big oven but they're happy to throw nuggets etc in the air fryer.
I also use it for roast chicken or marinated chicken pieces, toasties, garlic bread, reheating meals that would be better in the oven than the microwave (pizza reheats well in it). Greggs reheats well in it too, I've done pies and pastries a few times (both reheating them or cooking from frozen). I've warmed up fruit pies in it.
I've made chips and potato wedges from scratch as well as cooking frozen ones. You can use it to crisp up a baked potato that's been cooked in the microwave (although I don't like the skins too crispy but others do).
I boil eggs in it, I know boiling an egg is easy but it's even easier to chuck it in the drawer for 8 minutes and not need to wait for a pan to come to the boil and then time it carefully after that, the air fryer turns itself off and beeps at me so I remember about it. I've forgotten about pans of eggs multiple times before. 
I cook bacon and sausages in it, bacon crisps up nicely and like with the eggs, you don't have to keep an eye on it like you would with a grill or frying pan. Basically if you can do it in the oven or grill I usually do it in the air fryer now. It's only larger things like lasagne etc that I use my oven for now.