I have had virtually the same problem (on my Siemens, which is almost identical to the one on the pictures Penguin45 posted). Since we moved in to this house, a month ago, I have noticed that the machine fills water in short intermittent intervalls, but it wasn't until today it wouldn't start it's cycle. The evacuation pump just kept going.
And yes, there was water in the bottom tray. Draining it fixed the problem, but when I ran the machine with the left side cover off it was clear that water kept overflowing in the water level control chamber. The chamber was fairly clean, but I removed some sludge from the plastic tube (called transfer pipe earlier?) This helped, but it hasn't fixed the problem entirely. It still fills the water in intervalls, although longer between the cutoffs. And the water level still gets dangerously high in the control chamber, so much that a few drops escape from time to time.
So now I wonder, is all the incoming water supposed to pass the control chamber? Because the incoming water is divided into two pipes by the intricately shaped plastic tube thingy on the left, and it seems 95% of the water goes into the left of the two downgoing pipes, and then, as far as i can understand, it comes up again into the level control chamber. Should more water take the right route (which perhaps goes straight into the machine?), thus easing the flow through the control chamber? Any other suggestions?
(Different guy than the one just above, this one is from Sweden