"Much obliged" — Old-fashioned? Polite? Pedantic?

Solution 1:

In Britain it is a fairly normal everyday colloquialism, used in different ways. For example:

When someone has done you a favour: 'Thanks indeed, much obliged!'

A farmer speaking to someone who has asked permission to walk across his land: 'Yes, that's perfectly alright, but I'd be much obliged if you would close the gates behind you as you go'.

Reporting an experience to a friend; 'I felt very much obliged to the policeman who helped me get the car back on the road.'

Solution 2:

It is a reasonably common alternative to "thank you" in the American Southern regional dialects, based on my experience. It also has an old-fashioned feel courtesy of western movies, so some may use it in a tongue-in-cheek or archaic flavor to hearken back to that era.

"Much obliged, ma'am."

Solution 3:

Obligation means indebtedness, so to use it in the phrase "much obliged" is to say "I am indebted to you". I would say it is polite, but no more so than a prim "Thank you". It can also be considered old-fashioned; it originated some time in the late 1500s and became popular in the 1600s. It's used much less today. However, it's only slightly older than "thank you":

Google Ngram