The term is "offset drain" (i.e. not in the center), and it offers a couple of advantages. It allows you to set down, e.g., a roasting pan to soak, without covering the drain hole. Also, it allows more room under the sink for storage, trash, whatever, because your plumbing and disposal are not smack-dab in the center. I don't quite agree with Mikespringer. Typically what causes the plumbing to need to be retrofit from an older sink is the depth of the new sink (plus countertop which adds about an inch). Older sinks might be 6 or 7 inches deep, and as Mike said, newer sinks tend to be 8-9+" deep plus a thicker countertop than, say, formica was. Also, newer disposals tend to be bigger than the older ones. That means your older plumbing outlet position out of the wall could be too high. But moving the sink's drain hole 2-3 inches from the center of the sink to the back isn't as disruptive. I had an older shallow sink with a center drain that I replaced with a 9" deep sink with an offset drain in the rear right. Luckily, my plumbing didn't need any changes, even with the added depth of the sink, thicker countertop and big disposal. It just depends on your setup. I really like my sink's offset drain hole in the rear right. But it is more common to find sinks' offset drains in the rear center which is fine too. So I wouldn't worry if the drain is offset center or offset right; just having it offset is an advantage. There's only a few sinks I know of that are offset to the right, which are the Blancodiamond Supersingle in Silgranit (very large sink), the Elkay Elumina, some of the Shaws fireclay sinks and the Rachiele sinks. But you can easily find quite a number of sinks at all price points with an offset drain rear center.

akchi-town: Thanks for the note. Re-reading my post, I did not express myself clearly. "RR" was supposed to mean "right rear" (or corner-offset). I have indeed looked at Handcrafted Metals. In fact, I realized after I posted that I should have referenced them. I have not actually asked them for a quote, but the prices for their stock and custom sinks are still beyond what I was comfortably willing to spend. By not contacting them, I think I was sorta avoiding temptation, if you know what I mean! ;-) I think I will at least get a price from them, though. I have no real restrictions in size. I had originally been looking for a very small sink (21") to allow me to use a small cab, so that I could have room in my layout for other things. GW helped me realize I would be better to use a full-size sink cab (36") and eliminate a separate cab for recycling. Hence my need for a corner-offset drain, so I can squeeze recycling under the sink. I think my ideal size would be about 24 to 26". Funny, it seems to me that there aren't a lot of sinks in this range -- they seem to jump from 22 to 30". (Plenty of exceptions, of course.) Another desideratum that I didn't list in the first post was that I would prefer a shallower bowl, about 8" max. I like everything about the Elkay except two: I'd prefer copper, and I'd like what Franke calls an "integral ledge" to hold a grid or cutting board at an elevated height. My sister has that feature, and I love it. There is an interplay with size here: one thought is to abandon the integral ledge, and get a wider sink instead. Then I could put a draining rack off to one side in the sink to serve the same purpose. But this solution wouldn't be my first choice.

I think the center drain siligranite sink is undermount only whereas the offset drain one can be either undermount or drop-in. If you're planning to do undermount then it's really just personal preference. I have mine offset (and undermounted) and like it that way. I can load up dishes on one side and still access my drain and disposal. Without a disposal it probably makes even less of a difference.

i'm not really understanding what you're asking. different brand of sink will also have a center drain. you measure the distance from the wall to the center of the sink or just in front of the drain. that's your spout reach. if you tile the wall, take that in account if you measure. what size sink were you wanting to get (depth-wise)? i used a RH sink/vanity with my wall mount. the spout was about 8" or so. But I also used a 3/4" marble backsplash.