Because keeping all of those quotes, notes, and rumors in one post is getting lengthy, let's break this down by team in separate posts. As these come in, they will be updated and reposted.
Latest status: Depends on Brad Penny/Kyle Lohse
Lohse hasn't been placed on the disabled list yet, though that seems likely, and the Cardinals are going to have to move forward as if they have a hole in the rotation that needs filling. Lohse is 1-4 with a 5.89 ERA thus far, so an upgrade was possible anyway but now you'd have to expect that St. Louis is going to be a major player on the trade market. That means you'll hear Cliff Lee and Roy Oswalt's names attached to the Cardinals. (Update: Lohse will have surgery on his forearm.)
Rob Neyer (5/27):
But if Brad Penny doesn't come back strong in June, the Cardinals are likely to get into the Roy Oswalt / Cliff Lee sweepstakes, and hard. Unfortunately, the Cardinals don't have a great deal of talent in their farm system, so putting together an attractive package might be problematic. They probably just have to hope Penny's healthy and cobble together starts as necessary.
Matthew H. Leach (and here) (5/21):
No reason to use what resources are available (talent and payroll room) on a starting pitcher when that's the strongest part of the team. Do they put in a call? Sure, you have to. But to pursue seriously, doesn't make sense.