Your Green Card - Always, Always Carry it With You
Recent news that AMTRAK is increasing security on its trains as well as stories that DHS agents are profiling "foreign-looking" AMTRAK passengers and demanding to see identity documents serves as a reminder to permanent residents to always carry their green cards with them.
First of all--it's the law.
Secondly, and as a practical matter, if you are singled out on a AMTRAK train or a Greyhound bus and you don't have your green card on you, you're inviting big problems. At the very least, you're in for inconvenience and hassle; at worst, you could be detained.
Carry your green card with you at all times (and your immigration attorney's business card just in case there is still a problem). If you're not a green card holder but are otherwise here legally or if you have a petition or application pending to get yourself legal, carry proof of that with you--for example, copies of Immigration Court orders, I-797 Receipt Notices, copies of petitions, etc - anything that shows your legal status or your pending legal status.
Be careful out there.