Is it possible to determine one's ancestry (or at least the most probable ancestry) from their looks?

You can only do so vaguely like someone looks European or Oriental but don't every try to pin it down to specific national groups or ethnicities. People who think they can are going by stereotypes which frequently don't apply. For instance many think the Irish should be red headed and blue eyed. A common Irish type is someone with black hair, pale skin and blue or brown eyes, probably more common than the red haired Irish. You also see the black hair, pale skin among many English.

A Castillian Spaniard could be walking down the street of South Carolina and people would assume he was just another Anglo Saxon American.

I think there are websites that do like you state and they might be fun but not to be taken too seriously.

There are very tall Germans and short squatty Germans.

In genealogy we only go by documents/records. We don't even think about a person's appearance.

Not really, which doesn't stop people from asking "What is my heritage? Pic included." here 5 times a day.

You can tell race, roughly, most of the time. That's about it. Someone who saw a LOT of different people - I'm thinking a hostess at a coffee shop in an international airport, or a customs officer - could make a better guess than aveage.

If you fit the stereotype, yes; I'd bet a waitress or policeman in an area that had five or six tribes of Africans or American Indians could tell at a glance, 80% of the time. I could distinguish between Iban, Malay and Chinese when I was teaching in Malaysia, although people in the USA looking at my slides could not.

But, stereotypes are not always that. Look at the parachute regiment of the Israeli Army, and think of the stereotype of the Jewish school boy; quiet, meek, out-of-shape, highly educated violin players who routinely give bullies their lunch money. (It would be fun to watch a bully try to collect from a young-looking paratrooper.)

If the person has a look that is distinctive to their ancestry, then yes, you can. Of course, for every person that has looks that are consistent with their ancestry, there are probably several that either don't show any tell tale sighs, or maybe even other ones that aren't typical.

No it isn't, to be sure of your ancestry you need to research your ancestry to find out.

My father was very dark olive skinned and often was mistaken for italian ancestry, despite his very famous English names...........as his mother had died when he was very young, he didn't really know if she was from elsewhere than the UK...however I have traced it and he was 'all ' English all the way back to 1535 ( up to now) however who knows what I will find in the future