In the United States,
I also think that US Airways is the next major US carrier to dissapear, they don't seem to expand in adding new routes (they dropped Brussels). Everybody seems to think US Airways will go, and I'm convinced it will be gone before the end of the decade.
The five major carriers that are likely to stay are American, Delta, Continental, Southwest, and Northwest. United has lost a lot of money last year and was said to perish sometimes this year, but they seem to recover a little bit. I'm not sure about America West, they've been struggling a lot to survive in the nearly 20 years they have existed. Alaska could be taken over by American, Delta or Continental. Aloha and Hawaaian will merge, if they have not merged already.
In Europe, the four largest carriers that are likely to stay are KLM, Air France, British Airways and Lufthansa. I'm not too sure about the others.
In Africa, definitely South African Airways will stay.
In South America, Varig and Lan Chile have a good chance to stay.
In Asia and Australia, it looks like China Airlines (CI) will dissapear. Singapore, JAL and Qantas are likely to live long. Sure there are many other major airlines in that part of the world, but I mention the ones that have many chances to stay for a long time. I didn't say that all others would dissapear right away, Cathay, ANA and Thai do have chances to stay alive.