I'm looking for something like very slow expanding foam. The issue is an unavoidable cold joint/crack that I would like to have be perfectly air and water tight. Is there a bar/bead of foam that could be laid down before the second pour that would slowly expand in the presence of moisture (say over several weeks) to plug the crack? I'm not convinced that I can get post applied caulk in well enough to be completely effective.

Polyurethane glue, i.e. Gorilla Glue or Loctite PL Premium construction adhesive. Both cure in the presence of moisture and expand as they cure; although, not as greatly as spray foams. Cure time is on the order of hours rather than days or weeks though. Both are waterproof.

It looks like this is called a hydrophilic waterstop and will expand well after the new concrete has cured.

http://www.greenstreak.com/div3/waterstops/hydrotite.asp

You can install a bentonite strip, such as RX101. Bentonite can be placed at cold joints within the concrete core and gets poured in place. If any moisture penetrates the cold seam, it will encounter the bentonite, which expands when moisture hits it. I have used this product on foundation additions (between existing foundation and new one) in areas with high water table/potential moisture issues.

I know a few people who wish that that had been used between their basement floor and walls.

Hello all !

Ensuring that you have a clean top of wall before your next pour is the best practice. Not expanding foam, not ..., not....
Don't waste your money on something like mentioned above. No offence people. Been in the industry for awhile and from what I've learned debris left in the walls is always the cause for water intrusion. Wether it be cut outs from the walls to leaves from the trees, get it out of the walls.

Cheers!