This seemed kind of odd and confusing to us. Trains just don't go North or South, East and West. You can get off a train going West and get on the next on the same numbered track and it will go East. So, be careful. If you miss a stop and think you can just get the next train on the other side going back to that stop, don't count on it.
Stuttgart is a notorious automobile town (the Mercedes and Porsche factories are nearby), so it's no wonder we non-motorized individuals are treated as second-class citizens and banished into underground tunnels, as though we were rats or moles.
Even the central station (Hauptbahnhof) has a high-speed six-lane motorway passing right in front of it, with no surface-level crossing for pedestrians or cyclists. So to get to the station you have to go down an escalator (if it's working) or a flight of stairs (if not too many people are sitting on it) and find your way through a maze of passageways.
(We used to have this problem in Frankfurt too, by the way, but there were lots of protests and now we have equal and adequate time to cross the street.)
Another indication of Stuttgart's auto-mania is the fact that there is a Mercedes star on top of the clock tower of the train station. (Enlarge the photo to see this.)
On the roof of that tower there is a free observation platform (recommended) and on three floors of the tower there is a free exhibition about "Stuttgart 21" (see next Warning tip).
On three floors of the clock tower at Stuttgart Central Station there is an elaborate multi-media exhibition on "Stuttgart 21", trying to convince us that it would be a good idea to destroy the station and replace it with a space-saving underground mini-station.
Of course I don't want to discourage you from looking at the exhibition -- it's free, and there are some pretty pictures -- but please keep in mind that any time saved on the train would be lost as you tried to find your way up to the surface with all your suitcases or whatever. Notice that the stylish people in the fancy animations don't have much luggage, nor do they have bicycles or baby carriages.
Fortunately there is little danger that this hare-brained scheme will actually be implemented, mainly because it would cost millions of Euros that nobody has in their budget.
They wanted to finance it by ripping out all the tracks and selling the resulting real estate at premium downtown prices, which would have doubled the size of downtown Stuttgart. What they didn't take into account was the Law of Supply and Demand. Even I know that if you double the supply of something, the price is bound to go way down.
But we have to keep our guard up. One of the candidates in the current mayoral election in Stuttgart is campaigning on a promise of reviving "Stuttgart 21", and for other reasons he even has a good chance of winning.