Note: I am only recommending the airlines that I have actually flown. Other airlines may be fine. Also I strongly prefer the Asian airlines over US airlines in every case (except the excellent Jet Blue which doesn't go to Asia).

Singapore Air. The best airline I have ever been on. Great food and service. This is my top pick. They generally stop in Singapore (no shock there) and the airport is really cool. The airport can be hours of entertainment as far as shopping, lounging in parks, eating and generally gawking and how spotlessly clean it is. If you get stuck there for an extended time there is a short term hotel on site and short city tours available.

EVA. Not Eva but E-V-A. This airline is based out of Taipei and is a great value. It is a very good airline with good service. The food is a little odd for the westerner but not bad. EVA often has some of the best fares. If you have a lot of money first class is unreal including closable sleeping "travel eggs" with built in TV and sound.

Air India and Indian Air. There are both good airlines but will be your first introduction to India. If you take them your Indian initiation will start early. One thing that is really nice about both of these airlines is that they have a menu with several choices. The food is generally very good but it is most certainly Indian! Once I was offered a "western" menu option but I didn't choose it and haven't seen it lately.

Korean Air. Is a fine airline. It didn't make much of an impression on me either good or bad. If your best fare is with this airline I would not pass it up.

Thai Air. Another acceptable airline. It works. I would choose any of the above over it except Korean which it is on par with.