Well, firstly, if you're laning as AP, you need an Abyssal Scepter. If you're AD you need, Hexdrinker, Maw of Malamortius as soon as you can.
Second, you should probably be playing a champion with RELIABLE HARD CC. Annie, Lulu, Kassadin, anyone else with something like a STUN or a SUPPRESS. Do not settle for a bind, because she'll still be dealing damage.
Third, when she roams, follow her. Blow up the wave as soon as you can, and make sure you're there to help whoever she's trying to get fed off. If they die to her... I mean, you can only do so much about your teammates not being able to survive a katarina roam. Ping on your way to let them know kat is on her way. If they don't listen... well, that's their fault and there's nothing you can do.
Late game, encourage people to get Guardian Angels, all AP should have a Zhonia's. If she can't kill you, her cooldowns don't get reset and she may not be able to get le Kat Penta.
In lane, stay well under your tower. If you've been following what I've said this whole time, Kat should have a LOT of trouble diving you, and if she does you are free to do what you want to her until one of you dies. Stun her, polymorph her, suppress her; don't let her combo you. As soon as you see that shunpo, put down your cc. Prepare preemptively if you see her advancing. Unless you've got a huge lead and lots of MR, don't push the wave at all. Try to keep it close to your tower. If your junger wants to gank, ready your cc. If you're Annie, charge that stun, maybe just up to three charges just to do a quick shield > stun combo. If not, be ready on your cc to go all out on her. If your jungler is at high health, Kat shouldn't have the damage to deal with two champions early in the game. If your jungler sucks and dies... well... that's, again, out of your control. If your jungler tries to gank at 3/4 health or lower, ping them away, even if they're a tank. Again, you can't make him listen to you, so if he insists on going in, help him as much as you can without getting killed; if he's going down and Kat clearly isn't, head back to your tower and FAST. Pop ghost, pop flash, pop heal, do what you have to do to get back ASAP, because her cooldowns will be reset and she will blow you up.