I agree with the OP...it's one thing to ask a stranger/seatmate what he/she does for a living, it's quite another to ask for whom he/she works, for who are his/her customers.

When my stock response of "I'm a software consultant" doesn't stop the conversation, I pretty much politely but firmly say, "I'm more comfortable not discussing the specifics of my business with folks I don't know, I'm sure you can understand that...".

I would also comment in a broader context of this discussion: In 2007, are we STILL identified to people more for the identity of our employers vs. just what we do for a living?? I remember back in the early '90s when I worked for Compaq Computer Corp., I attended a third-party training class, and at the beginning of the class everyone of course had to go around the room and introduce themselves. Person 1 works for a plumbing supply company, person 2 for a small local banking institution, etc etc companies you've never heard of or are not conversation-worthy, and then it comes to me, and I work for Compaq. Suddenly, EVERYONE decides that I'm the person they have to b*tch to about the problems they were having with their computer, or customer service, etc etc. I finally had to rather rudely tell folks, "Look, I support a particular specialty for them, I can't address every issue you have with Compaq!"

OK, I get it: In conversation folks like to find common ground they can relate to, and if you work for a company someone's heard of then there you have it, but I still wish folks were more interested in the "what" than the "who". I know I am when I talk to others.

Now, having said all that, I must admit I've done some of my best "networking" with seatmates on planes, esp. since I achieved Plat and started sitting up front more often than not, but still, for me it's about "what I do", not "for whom I do it".