Tom's just being provocative. I am a big fan of Gullane #3, and it does have excellent green complexes (as a 5000 yard course MUST have). But best. No.
The Old Course greens are the most interesting, but only because they were largely NOT designed (or if designed, designed for the Reverse routing...). However, nobody would build anything like them today, and rightly so.
The internal Machrihanish greens are wild and fun, but "great" is not the word for them. They aren't part and parcel of holes designs whcih make the golfer think strategically from tee to final putt.
The greens at Turnberry, Muirfield and Carnoustie are largely subtle (bland?) rather than interesting. Getting there (i.e. driving) is what counts at those courses.
The best? Dornoch. Interesting, fun, and as good as it gets linkage of tee to hole strategic thinking.
Rich:
I can't comment on Dornoch's greens, and thus can't compare their strategic merit relative to Machrihanish. But I'd quibble a fair amount with the notion that its greens don't play into strategic decisions.
On 3 (Islay), the very large green is angled from front right to back left, and you clearly want to be on the right side of the fairway for a better approach. But that means a decision about whether or not to carry the very large ridge that bisects the fairway at an angle that also runs right short to long left. The approach from the left also requires a carry over two visually intimidating pot bunkers. The flow and design of the hole say, you're better off with an approach from the right, but there is way more room and less danger off the tee to the left. That's a pretty good design, in part created by the angle of the green.
On 4 (Jura), the par 3 is not a great short hole, but a good one, because the green surrounds are so penal -- steep falloffs in every direction, and three pot bunkers -- two staring you in the face on the tee -- that need to be avoided. The green's contours are more subtle than dramatic, but the green site is a good one for what is a target hole.
On 5 (Punch Bowl) -- good golly, this is a great hole, with a great green; a more interesting par 4 than anything I saw at TOC (!!). That false front is just enormous, with huge consequences for underclubbing. And if you've only won half the battle once you're on the green -- severe contours and falloffs back and right of the green that suggest a careful approach from what is one of the most topsy-turvy fairways around, and thus a likely uneven lie.
On 7 (Brauch More), the doglegging right fairway is contrasted by a green angled away from the line of play. Again, the preferred angle in is from the right, and that's where most of the trouble lies. Too far left on the tee shot requires an approach over a sand dune, and also makes the green more shallow. An approach from the right opens up the green, and allows for more error, but you risk the rough, fairway trap, and mounds and gullies right. A great design of a hole -- set up by an interestingly placed green.
On 8 (Gigha), it's all hit or miss for that green, so you better be in the fairway on this short par 4. Severe uphill approach to the green, and falloffs all around the sides and back, and a nasty little bunker front right.
On 9 (Ranachan), it's pretty similar -- falloffs back and right on the greensite, a series of bunkers left, and another right front pot bunker that's trouble. And it's one of the smallest greens on the course.
On 10 (Cnocmoy), the smallish green, and two pot bunkers that narrow the entryway, force a decision on both the approach and the tee shot -- try to squeeze the tee shot through the mounds at @ the 250-yard mark, or layup short of them, then another layup. Played as a three-shotter, and the green is not troublesome. But it's a short par 5, and one is tempted to take it on in two.
On 11 (Strabane), golfers are confronted with a reverse Redan-esque hole -- a nicely angled green, very deep, with bunkers left and right. At 192 yards from the regular tees, it's a strong hole.
12 (Long hole) is another terrific green site -- severe drop-off before the green, which leads to two bunkers, big sand dunes left and right, falloffs and depressions all around, big contours internally. Another shortish par 5 that gets really interesting from about 100 yards in, mainly because of everything that's happening both in and around the green.
13 (Kilkivan) has a severe false front, bunkers fronting left and right, and falloffs left and back. Another "better be in the fairway" tee shot.
15 and 16, the two back nine par 3s, are also terrific holes, with greens sitting perched up from their surroundings, and bunkers -- several on the short 15, one big one on the long 16th -- coming into play.
Even 17 and 18, probably the two weakest holes on the course, have stuff going on around the greensites that make for some thought-provoking decisions on the tee (18, for sure) or on the approach (17).
Still hoping to get to Dornoch, though, to compare!
Ed -- I'd agree about Dornoch, but I have to contend with a household veto!