I wouldn't say it's "archaic". It's a bit over-formal for modern use, and the etymology of the expression is a bit foggy, but it still has it's uses, when one wants to be a bit formal without bowing and scraping.
– Hot LicksMay 26 '15 at 16:20
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It could be replaced with "Highly obliged" or simply "Obliged" but even these words are considered overly formal and archaic. In modern English, one simply uses "Thank you", "Thanks a lot" or rarely "Many thanks".