Updated January 2000
As far as long-distance Amtrak trains are concerned, there is the corridor, there is the Capitol Limited, and there is everything going south. All of the latter are best seen in Alexandria, although you can see them pop out of the ground south of the capitol. The Cap. Ltd. is best seen in Silver Spring, because once it gets much west of there it is going too fast to be seen to well. There is often private car traffic on this train.
The trip up and down the corridor isn't terribly scenic, although it is about the only way to see the Ivy City yards. I've taken the Capitol Ltd. out west and back, and it offers varying scenery. On the trip out it unfortunately crosses the mountains mostly at night, but (if you like that sort of industrial stuff) you get a great view of the Gary steel works. On the way back, the mountains are crossed in the morning, and the scenery is glorious, particularly in the spring and fall.
I'm told the Cardinal has even better mountain scenery, but I cannot say anything about this first hand.
MARC tickets can be bought on the trains at a premium, or at the stations with offices. Single day tickets are pretty steep. Penn tickets are accepted on the Camden line, but not vice versa. Ticket offices are generally open only in the morning, except in DC, New Carrollton, Baltimore and BWI (and in several other places listed on the schedules). Tickets can also be bought at the ticket office in the U of Md. ticket office, in the Stamp Union. The best MARC action spots are along the metro Red line, at New Carrollton, at Gaithersburg, at Laurel, and at Point of Rocks if you can get there. (These last three have particularly good sight lines for photography.) The spot I mentioned off Brookville Road on the south side of the line in Silver Spring, near the stub of the old Georgetown Branch, is also good in the evening.
It should be noted that the old MARC site referred to by most is defunct; not only that, but the old official site has also moved. My link goes to the current official site (which isn't very good unless you're a commuter).
The Virginia Rail Express (VRE) runs only in the rush hours. Most of the stations are simply post-modern platforms. This is strictly a commuter operation and uses a self-service ticketing machine. The paint is very snazzy; one can see the trains laying over next to the metro yard at the bottom of the Ivy City yards at Union Station. The station at L'Enfant Plaza is a super place to watch traffic to/from the south-- unless it's a cold windy day. They are about to receive some strikingly ugly Kawasaki double-decker cars. (They have a super website, in contrast to the MARC site.)