I was at Doonbeg before it opened, so I didn't play. I can't imagine the greens were that fast, but it still had several which were so severely contoured that they looked ridiculous ... the fifth green is huge, but I think there are only about two places to put the hole.
I'm not a fan of Ballybunion New either ... it's torture for me ... but mostly because the greens are so small. The contours really aren't that extreme, but if you're more than ten feet from the hole you'll probably have to putt over something.
The greens at The National (the original course) are very severe, most of them divided laterally into two or three sections by steep ridges ... the kind of thing where you have to risk not getting over the ridge and missing by 50 feet, or being resigned to going way past the hole once you do get over the ridge. They're "greens within a green," as Tom P. says -- extremely narrow ones! I'm a really good putter, but the last time I played them, they were too much for me.
I'll go back to Lynn Shackelford's comment about Rustic Canyon (which I haven't seen). I don't think every green should be built so that you can always get it close from anywhere ... that's "fairness" at the expense of strategy. But I don't think you ought to find very many situations where you can't get a putt within six or seven feet if you hit a really good putt, and give yourself a chance to two-putt.
My most famous green for three-whacks is the fourth at Lost Dunes (a short par 5 where a lot of people have made two-up and three-in pars). But even there, in most cases it's possible to get the first putt close. If the pin is back left upper tier, and you're on the front of the green, that's the worst case -- you have to choose between risking not getting up the tier, or deliberately putting it ten feet past and trying to make the comebacker. I think that's okay on a short par 5; in fact, for a pretty much dead flat hole along the boundary, the green makes it a very interesting (if controversial) hole.