Foamer: A train and railway hobbyist.
From a New York Times travel feature by Andy Isaacson about riding Amtrak across the United States:
That sentence suggests that foamer derives from "foaming at the mouth," but a retired locomotive engineer who goes by "Hoghead" sets the record straight in Yahoo Answers:
The Western Pacific (now the UP) runs the "Feather River Route" eastward along the Feather River to Portola and beyond. The timber industry has now been gutted, but at the time there were a lot pollutants being dumped into the river upstream, primarily waste from mills and stagnant log ponds.
This caused the formation of copious amounts of foam in back washes and eddies along the river, a favorite place for rail buffs and photographers.
Often times, these people would wade into the river to get the right angle for a photo, usually knee deep or deeper amidst the foam, hence the moniker was applied; "Foamers." Its meaning has been upgraded to describe an over zealous aficionado of rail operations.
Foamer is North American slang, used by rail buffs (sometimes called railfans) as well as non-enthusiasts. (The pejorative term is FRN, for Fucking Rail Nut.) The UK equivalent is trainspotter. (Off topic, but interesting: the birdwatching world's equivalent is twitcher.)
P.S. I wrote this post over the weekend. Quite by chance, Monday's poem of the day on public radio's Writer's Almanac is "Trains," by David Shumate.