I have brought my bike on the Downeaster (Portland - Boston) a few times. You have to make a reservation for the bike, and pay a fee ($5 if I remember), and then they let you take the bike on the train. You have to take it on and off, but it was no big deal, even for my bike, fully loaded with panniers.
I have also taken a folding bike on trains all over with never a problem (including the Monorail in Vegas), on the Vegas monorail a cop got on at one station and was closely eyeing the bike (folded up). I asked him if there was an issue with bringing bikes on the monorail, and he said, 'not cute ones like that which go through the turnstiles'.