We did a counter-depth-stainless-apron-front-flush-mount sink. You could do that with a wood counter top too. I detest that thin strip of counter at the front and back!

I saw a sink like you described on a site which sells diy slabs of granite (muranocollection). It is made so that no hole needs to be cut in the stone, but the stone just butts up to the sides of the sink unit. Seems like it could work for wood as well.

Here is a link that might be useful: Murano Collection

Pharoah: do you mind sharing what sink you have?

Thanks for the suggestions. The Murano sink looks like it might work, but unfortunately there aren't any dealers in my area.

Additional info about specific manufacturers/models that might work would be most appreciated.

I don't understand why this is not a more common configuration. It makes so much sense. Here are a couple of others to check out:
Blanco Wave Plus Module Sink
Kindred KCWD6016R-9 Double Bowl Countertop Kitchen Sink With Drainboard
Elkay Lustertone Sinktop - comes in several lengths
Another thought.... have one made; order a real short corian (or simular) counter with a built in sink and maybe cut in runnels, butt the wood right up to the corian section. It might work.

Endlessfixing, I'm searching for counter depth sink options as well--and with not much success unless I want to invest $2-3K in the sink alone (Kohler's Taskcenter). I haven't checked out mulemom's suggestions yet, but Kohler's Taskcenter(s) are options--if you don't mind the prices. A couple of people on this forum found Taskcenters on Craiglist, but no such luck for myself. The Ikea Domsjo doesn't fit my pennisula countertop w/o building the countertop out more to MAKE it work.

Elkay also has a series of "Gourmet" sinks--also pricey. Pharoah's sink can be found at this etailer: http://www.contempolivinginc.com/ststkisi.html

Good luck to you--

I've noticed that this type of sink seems more common in the UK. Planning a trip anytime soon?

http://www.rangemaster.co.uk/index_437.htm
http://www.rangemaster.co.uk/index_439.htm
http://aprilskitchen.co.uk/ovw_main.asp?xREC=1692&NewId=1&PTYP=Sink

Thanks for all the info. Most do seem pricey, so I'll keep looking.

I'm going to look into Mulemon's suggestion about a corian built in sink and counter.