This is the point of situational items. If you find yourself getting killed a lot by his Ult, then get MR items. The point of the game is to adapt to win, not stubbornly use the same items over and over. If you are dying from magic, get more MR. If AD carries are wrecking you, get Thormail. There is no cookie cutter method to victory against skilled players.

Doesn't Annie have a shield that gives her MR?

Seriously though, buy some defensive items occasionally. An Abyssal Scepter works wonders against Karthus as Annie.

Of course, some people just have problems deviating from their damage items because they think they should never have to buy defensive items unless they are the tank.

By HP awareness I mean don't hang around with 200 or less HP once he's hit 6 and you know his ult is off CD. If there's a teamfight going on, and you suspect that he has his ult up, retreat with more HP than you usually do. If you think it's a bad idea to 'maybe' not die and feed his Mejai's stacks, then I can't help.

Annie is better built tanky than pure AP, anyway. I usually get a RoA and a Veil and still do fine. As for it coming later in the game... well, if you're up against AP users, especially the ones who rely on single nukes or spell combos, you shouldn't wait to get MR and maybe a Veil. You should shut down their damage ASAP. Especially if they buy snowball items. As I said, you don't need a Veil early on, but getting a Negatron Cloak fairly early, or some HP (RoA for Annie), helps a ton. Counters their initial magic penetration (which they get from runes and masteries), and forces the opposing casters to invest in more magicpen.

There's no way to 'avoid it' other than what we've already posted. If you think those things are situational, and shouldn't be used as common counters I can't help you more.

Adding to what I said, if you think about it, Karthus doesn't really have anything going for him other than his ult. He has a nuke which is strong, but can be avoided fairly easily. He has a wall which is also fairly dodgeable. And his Defile puts him in harms way.

He's a lot harder to play than Annie, too. ^^

When I play Janna and Karth pops his brainless ult I usually look for the lowest HP person and shield them, it saves them sometimes.

It just sucks when there's multiple people with low hp, you know someone is going to die to the nonsense.

If you are walking away from the battle with that little HP, then anything can get you. Karthus's ult is the only thing that makes him great. Without that, he would be completely crappy. Every champ has things that makes them unique. I agree that sometimes it sucks, especially when he does it from his grave and gets the occasional penta kill. Unfortunately, that is how the game goes sometimes. You have to remember, through the course of the game, this doesn't always happen and if it happens a lot, you need to avoid that situation by monitoring your life more closely when you know his ult might be ready. Sometimes you can block it, sometimes you cannot, but as mentioned earlier, it shouldn't always happen to you.

Alpha Strike does, if you notice Yi, when he uses Alpha Strike temporarily disappears from the map. Basically, it means he's not there, in the game, at the moment, at that moment. It's weird, but that's how it is. Flash does not pop projectiles anymore so i do doubt that works anymore =(