Updated January 2000
North of town, near Glenmont on the Metro red line, we have the National Capital Trolley Museum, which has a nicely eclectic collection and some good static displays. Their website provides good directions, if you can get the map to load.
Other than the garage and being on a train, there is unfortunately no good spot to watch the activity from. I don't know about the neighborhood, but the only spots where you can see the tracks well require trespassing. It is possible to go around on the left side of the building, past the old Woodies warehouse, and in the next block there is an empty lot with a fence around it. The far edges of this lot are an old coal dumping track, and the embankment leading to the tracks themselves. There is apparently some other equally illegal access to the tracks closer to where the tower used to be. At any rate, the only thing to be seen on this side is the signals at the west end of the wye.
The other side seems to be even worse. The tracks heading to Baltimore provide an effective screen of the yards.
You can go around the south side of the capitol and see where the trains enter and leave the tunnels from the south. Further along is the VRE L'Enfant Plaza station, which is bitterly cold in the winter but which has a long unobstructed view and a signal bridge to boot. You should consult an Amtrak and/or a VRE schedule before bothering with either of these, because there is very little freight on this line.
The Red line has two sections which parallel the ex-B&O line going West. The Shady Grove end is not that interesting; the Silver Spring end (starting from Union Station) passes lots of interesting stuff, almost all of which is on the north side of the track. The Orange line to New Carrollton parallels the Corridor; not too many trains but lots of interesting trackwork, including the only 100 mph speed limit signs you are ever likely to see. The Yellow Line crosses the river parallel to the RR bridge, and affords an interesting view of DC from the river; it then has a great view of National Airport. The other end of the Orange line and all of the Blue and Green lines do not show any rail sights, although the section of Green line to the north parallels the ex-B&O line to Laurel for a ways.
There are a number of metro yards. The one on the Red line between Union Station and Rhode Island Ave. is plainly visible from the metro and nowhere else; another is in Glenmont, tucked behind a garden apartment complex and is not very visible. The one at the New Carrollton end of the Orange line is not very visible either. The Yellow line yard is behind the Norfolk Southern yard; if you are feeling adventurous you might want to try getting off at Eisenhower Ave. and follow the bike path west. I doubt there is really much to see. There are only two flavors of car, which are almost identical. Most of MofW equipment seems to stay at the Union Station yards.
At present there are six junctions, four of which are underground. The one outside the Pentagon station is interesting because it is so close to the station; the two tracks run on different levels through the station. If you look to the west you can see the other tracks come in and the levels change. The east blue/orange junction is pretty straightforward; the other is basically like that at Pentagon, with a bi-level station. I believe that the green-yellow junction at L'Enfant Plaza uses the same principle, but it is farther from the station and harder to see. The yellow-blue line junction just before Eisenhower Ave. is above ground and is the only readily visible wye in the system. Just before the Pentagon Station on the Blue Line, there is a short stub tunnel which is intended to accomodate a possible new line, if there is the money. If you are riding in the front car and peer through the driver's windows, you can catch a glimpse of it. There is also a connection between the green and red lines at Fort Totten (that's what the seemingly useless strip of track is for that dives down between the red line tracks just east of the station). This is the track that used to allow the green-to-red express service during rush hour. The final junction has no purpose except to connect the whole system together; it joins the blue/orange line to the red line in the vicinity of the two Farragut stations. You can get a very brief glimpse of it if you sit on the right side of of a red line train, facing back toward the station, as you head toward Shady Grove. Just as you leave Farragut North, this track will appear out of nowhere and merge with yours.
Two other oddball points are the junction with CSX and the hidden station on the Red line. The CSX junction is at the Union Station yard, and requires two trips on the red line to see it all. On the way out to Rhode Island Avenue, you need to be seated at a window on the left, facing forward. As you climb toward the station, you can see that one track from the yard dives into a cut and stops, and there is a little bit of track going back up out of the cut and under the decending Metro track going the other way. Off in the distance you can see QN Junction; note that one track peels off the mainline and splits, with one branch heading straight down the metro tracks and the rest curving around to the right of the track you're own now. If you go back the other way, you need to be on the right at a window. Keep an eye on the track that peels away to the right; several tracks peel off of it, then just before you get down to ground level, you'll see a trailing point switch which leads off into a gate. That track is the one that leads into the metro track you saw going the other way.
The hidden station is where they take the money at night. It is between the Metro Center and McPherson Square stations on the Red line, and it is very hard to see, even if you know it's there. You have to sit on the left side of the train and watch for the break in the pattern of tunnel lights.
If you want useless trivia, the escalators at the Wheaton station are supposed to be the longest in the free world. They are very slow. The red line station at Forest Glen is allegedly the deepest in the world, depending upon where you measure it from, and is the only station with no escalators.
WARNING: The metro doesn't run all night; it closes pretty early on Sundays. Don't get stranded.
There has been persistent talk of turning the Bethesda to Silver Spring portion into light rail, which, if you look at the Metro map, makes a great deal of sense. In the meantime, the trail offers an interesting look into a B&O backwater.
There are two stations of interest on the VA side. Manassas is interesting but is a long drive; it is served by Amtrak. Alexandria King St. Station is easily accessible from Metro on the Yellow line.