First off, in general it's important to remember that for non commercial use, photography of anything that you can see from public property is fair game to take pictures of.
Read this (and I keep a copy of it in my camera bag - I haven't, but really should also keep a copy of the photo policy for wherever I'm shooting in the bag as well).
Amtrak's official policy can be found here.
It's pretty photographer friendly, however I have a bit of an issue with it. In part, it states:
I don't like the italicized bit because for seemingly any reason a crew member that doesn't like what you're doing can tell you to stop and you have to oblige them. I'd try to make the convincing argument that I'm not interfering with passengers or crew, but at the end of the day you're at the mercy of the crew while you're on board a train.
Ticketed passengers on board trains may take photos or video record on a train when it does not interfere with passengers or crew and in accordance with any directions given by Amtrak onboard train personnel.
WMATA (Washington, DC):
I'm well aquainted with WMATA's policy, due to this incident (which is surprisingly on the first page of results when you Google "WMATA photo policy"). The policy can be found in this 128 page PDF.
The relevant portion is section 100.8 and is mostly focused on regulations concerning commercial style filming. The only reference to non-commercial photography comes in section (2):
Still photography that does not require a tripod, special lighting, film crews, models, impair the normal ingress/egress or operation of WMATA services and can be accomplished by a hand-held camera by one person is not regulated
Basically, no tripods and stay out of the way. There have been some issues with people getting harassed about flashes in the face of train operators in underground stations that makes some sense. There's nothing that says whether a standard camera flash is considered "special lighting", but I suspect that they could make that stick and make you turn off the flash.
Maryland's official policy can be found here. I don't have a lot of experience with it (because I haven't had any issues), but apparently the officers up in Baltimore are a little more overzealous. The ACLU recently announced that they planned on suing the MTA based on their harassment of a tourist. The MTA was quick to respond with their photo policy and some excellent statements by the Chief and MTA Administrator. The gist of their photo policy is that it's perfectly OK as long as you're not being unsafe:
No permit required: A permit is not required for non-commercial, personal-use filming or photography by the general public that does not interfere with transit operations or safety.?
Please feel free to add to this list with the regulations for other agencies. It would be nice to have a reference to go to when traveling. It's up to us as photographers to be aware of our rights and assert them when necessary.