I think those are called "adventitious roots", that arise along the stem. Certainly tomatoes, and to some extent peppers and eggplant do it. They can, in principle, do it from anywhere along any stem. I believe it is actually somewhat rare in peppers and eggplant, however, as in, don't bet on it. I believe cucurbits can also form adventitious roots, but they don't do so below the soil line, and only do it at stem nodes. So I guess once those node roots start to form, you can try to bury them.

Consensus seems to be Solanaceae, Brassicaceae, and Cucurbitaceae so long as they branch from the stem rather than from the base.

Particularly helpful previous discussions, for easy reference:

http://forums2.gardenweb.com/discussions/1407918/vegetable-transplanting-deep-planting

http://forums2.gardenweb.com/discussions/1432530/planting-squash-seedlings-how-deep

http://forums2.gardenweb.com/discussions/3882325/do-you-plant-peppers-deep

http://forums2.gardenweb.com/discussions/1423318/how-deep

But again, tomatoes do this regularly. You can count on it happening with them. The others don't. You can bury them deep and they may or may not root from the stem.

I would disagree on that statement, daninthedirt. If you plant a Brassica seedling up to its first set of leaves it will root from the stem. In my experience you can count on it. It is a recognised technique when planting winter Brassicas which must withstand the winds of winter. A cabbage stem will even produce roots if left in the fridge overlong.

Well, I've never seen it happen for me in growing collards, and it is furthermore commonly reported that tomatoes are far more likely to root from the stem than at least other Solanaceae. But I'm willing to accept that one can be more successful with Brassicas.

As I said above "rooting along the stem" is only one of the many benefits of deep transplanting so that one issue shouldn't be the primary, much less, the only focus to the question.

Dave

It can be strange, for example I've had it happen with peppers many times, but some pepper plants didn't sprout any more roots when planted more deeply. I've also waited too long to hill potatoes, they had grown quite a bit, and when I hilled them they did not produce any advantitious roots. I think there's a mechanism at play in some plants in regards its maturity when you make the attempt.