I'm a cat person - if my avatar hasn't already given me away - so most of my pet knowledge comes from having three of the little devils wandering around the house. I love them dearly, though!
One of the big issues, particularly those who have long-haired cats is hairballs. It's fairly gross to hear your cat hacking like they'll cough up a lung, only to see a big blob of cat fur poached right onto your carpet. If that visual was enough for you, here's a great way to help with that.
If you don't have them on a specific diet, a hairball control food might work, though I have found that fairly ineffective with my cats. Instead, I use a dab of Vaseline on the bottom of their two front paws. The kitties will lick it off and it helps coat their throats, which makes it easier for the hair to go down. It also helps keep it down, if you know what I mean.
Not to worry, the Vaseline won't hurt your kitty. Some might not like it very much, while others may positively love it. If hairballs continue to be a problem, you may want to seek the advice of a vet, but I've significantly reduced the number of hairballs my cats have coughed up using this method. Hope it works for you!