Some good shouts in this thread. The Haunting was a revelation to me when I first saw it - that and Night of the Living Dead are the only black and white horrors I still find effective. Bear in mind that pretty much all of the characters in The Haunting are very un-PC in this day and age, but if you can look past their odd behaviour in the opening third, it's a very effective straight-up chiller.
The Shining and Poltergeist are also essential horror films, but are so well-known that I'd expect anyone with an interest would have seen them already.
Personally I found the first Ring film (Ringu as it seems to be known in the States) unsettling - I'm a big fan of its sound track and think that contributes a lot to its creepy air. The second film is not nearly as good though, and breaks the first film's premise, so I'd advise against that. And the prequel's just a blatant cash-in, although one or two of the effects are neat. I did quite enjoy Dark Water, by the same director as The Ring although it's not nearly as creepy. Still an above average supernatural thriller though.
FWIW I did much later also see the American remake of The Ring, and found it to be pretty faithful with the only changes made to make it easier to follow the plot for westerners, but it doesn't use any of the original's sound effects, so I didn't find it all that creepy, but still a decent film.
Another foreign film I found pretty creepy is an odd Spanish horror called
The Baby's Room which I gather was actually a TV movie over there and only seems to be available on an oddball compilation DVD with five other much worse films, only released in Spain or the US. It's worth tracking down though, particularly if you like your horror films spooky and a little twisted.
Oh, and I also quite enjoyed Triangle which is a slightly budget psych horror, that makes more than a couple of nods towards The Shining, which gets any films bonus marks in my book. Not sure it's a well respected horror, but I enjoyed it. British director too.
Also, I have a penchant for dark humour in my horror films, and I laughed my way through Drag Me To Hell when it came out a few years ago. If your friend liked the Evil Dead films, it's definitely one for the list.
So there you go: from the straightforward original to the overtly post-modern, take your pick.