In the US a "thank you" is all you hear in return for a compliment. Only here in Germany compliments are perpetually played down: "oh, this dress was on sale, nothing special".

@Werner, zum Glück ändert sich das allmählich. In meinem Freundes- und Bekanntenkreis wird sich auch einfach nur bedankt. Ich kenne dieses Herunterspielen nur von Leuten aus der Generation meiner Eltern (bin 30).

but there IS a difference!
Because if you say "Ich fühle mich geschmeichelt", you indicate that you really didn´t expect to get a compliment like this and you´re maybe a bit surprised.
This is getting lost if you just say "thank you"

Hannah, you could just say,
Wow, what a nice compliment. You can leave off the "Wow" if you prefer.
There's nothing wrong with saying I'm flattered or I feel flattered. They don't really sound old-fashioned, just kind of formal or stiff to me. But it depends on the background, age, circumstances, cultural differences, etc. as coldfinger and Werner pointed out.

This is colloquial, for sure, goes in the direction of "ich fühle mich gebauchpinselt",

Depending on the situation this might show some self-irony.

You could also say 'flattery will get you nowhere', or just blush.

... I bet, you say that to all the girls.

Hi Bacon..."chuffed" is very N.England...do the Americans know this word?

Oi, suziq! Don't have the foggiest - I fear not, though ;-)