Paul Leim gives a demonstration of a train-beat at a fast tempo in the second half of this video.

Songs exhibiting such a rhythm include:

The Devil went down to Georgia – Charlie Daniels
On the road again – Willie Nelson
Petticoat Junction – TV show
Last train home – Pat Metheny
Two Step – Dave Mathews Band
Gallows Pole -Led Zeppelin
Train Time - Cream
Trouble on the Line - Sawyer Brown
Train Kept a' Rolling - Aerosmith

(from Drum Bum)

somewhat off-topic, but a great train beat idea:

i got this from a good friend of mine.  it's originally from john dietrich of restless heart.

r l R l r r L r/r l R l r r L r  (caps are accents on 2 and 4)

Yeah, but all his backbeats seem to be with his left hand. I agree that the video timing is a little off, but to me it looks like one of the main patterns he plays is this:

l r L r  l R L r  l r L r  l R L r

Obviously he has to break that pattern up to do all those right-handed cymbal crashes, but that's what it looked like to me. Interesting!

train beats are my favorite beat to play on my standup kit, with brushes.

"Ready Steve?   Andy?    Mick?   Alright, fellas ..."  and how could we forget The Ballroom Blitz ... lots of country rock bands play that one, ya know ...  

Bart- Paul is a lefty playing righty. I am too, however I play the train with a right hand lead. I am just all messed up!

ok. confession.  here's a silly trick i used to do

i'd say, "who wants to hear a train!"...then i'd beat on the coffee table:

    right  left  RIGHT left  right LEFT RIGHT left

(starting reeeeallly slowly, just like an actual train, then gradually speeding it up til the train is at full speed, and i go "choooooo---chooooo!!!", then gradually slow it back down til its reaaaaaallly slow, then stop.

True. But you can also get a kind of cool pseudo half-time thing going by playing all quarter notes with the bass, and 2 and 4 with the hihat (half as fast as the snare backbeats).

COUNT: 1 e & a 2 e & a 3 e & a 4 e & a

SNARE: r l R l r l R l r l R l r l R l 
BASS:  x       x       x       x        
HIHAT:         x               x

But Jon E's boom-chic suggestion IS the most common way to play this groove.

COUNT: 1 e & a 2 e & a 3 e & a 4 e & a

SNARE: r l R l r l R l r l R l r l R l 
BASS:  x       x       x       x        
HIHAT:     x       x       x       x

There are some seriously wicked bass drum patterns at the end of that tune.

Makes my ankle hurt just thinking about them.  

Fishman of the band Phish plays a really awesome train beat on the song "Get Back on The Train".

cnt :  1 e & a 2 e & a 3 e & a 4 e & a
hh  :  x   x   x   x   x   x   x   x
snr :  l r L R l r L r l r L R l r L r
bass:  x     x x       x     x x  

Get this one in the pocket and I assure you your skills as a drummer will increase weather you want them to or not.

Hey, Mr A - how do you get your tab to line up? I did it once, but I had to use hyphens to indicate rests.

Mr Gobar - are those bass drum notes "and-uh" or "uh-two?"

Thanks - I think I tried to just set it in Courier:

(pre)

cm: o
hh: xxxxxxxxxxxxxxxx
sd:     s       s   
bd: k         k     

(font=Courier)
cm: o
hh: xxxxxxxxxxxxxxxx
sd:     s       s  
bd: k         k    

That's like a Samba train!

That's cause it's building steam, leaving the station.
Not your typical train beat...
 

If you use the Teletype function, see the button when you post, it will place these tags around your tab and make it line-up properly. It's so small, you'll need to increase the size a bit, as Mr. A suggested.

Example:

would look like this when posted:
R L R L

This is what I use, and increase the font size to 3, which would look like this:
R L R L

Or increase to 4:
R L R L

Anyway, it all lines up now as you add various lines in your tab notation. You can also use bold, italic, and colors as needed.

I agree gobarr!  I like to play 2 bars of train beat--2 bars of fill (keeping the feet going of course), or 4 and 4.  Whatever.