Inspired by this question, are there any known planetary systems with largely varying planes of orbit? For example a system where two planets have perpendicular planes?
Many planets have been found where their orbital axes do not align with the rotation axis of their star. This is achieved using measurements of the Rossiter-McLaughlin effect in transiting systems or by observing planets transit over spotted features on a star's surface.
As the stellar rotation axis is highly likely to coincide with its protoplanetary disk axis, the planets must (now) be orbiting out of this plane and some are retrograde. About 1/3 of hot Jupiter's are misaligned in this fashion.
It seems likely that many of the misaligned hot Jupiters could have planetary siblings orbiting further out that are more nearly in the rotation plane of the star. On the other hand, whatever event caused the misalignment could have wrecked the planetary system.
There is at present I think only one solid example where the measurements suggest non-coplanarity and that is in the planetary system surrounding Upsilon And A. Using radial velocities and astrometry from the fine guidance sensors on HST, MacArthur et al. (2010) were able to establish that the c and d planets (i.e. the 2nd and 3rd planets in the system) were inclined at angles of $30\pm1$ degrees with respect to each other. This is much larger than the differences seen in our solar system (maybe 7 degrees).
I'm not sure we know. I think that the methods used to detect planets orbiting other stars don't allow a determination of the plane of the orbit. One method involves noticing eclipses of the star by the planet, but planets orbiting in different planes, which both eclipse the star, would look the same as planets orbiting in the same plane. The other main method is looking at the Doppler shift of the star as it "wobbles" in response to the planet's gravity. Since that only allows a determination of one component of the velocity, I think it also doesn't allow a determination of the plane.
One way to tell would be to watch a system over time and measure perturbations of one planet's orbit due to another planet. Those perturbations would be different depending on whether the planets were in the same plane. But I think it'd be easier to get a "null" result (the planes are close to the same) than a positive result from this method: if they're in different planes, I think the perturbations would be too weak to observe, and it'd be hard to draw a firm conclusion from your failure to see them.
If the planets are all formed from a simple accretion disk, they should end up very close to the plane of the accretion disk. A planet with a different orientation must have had a different formation history, or to have suffered a severe deflection of its motion. IIRC one observed disk around a yound star was thought to be orbitting in opposite directions, i.e. the close in part going one direction, and an outer disk going in the opposite direction. But if you read Ted's answer about detection, the chances are very high that we would only see the planets from a single plane, and be unaware of any out of plane objects. The chances are that to get two accretion disks with different orientations (possibly at different times), you would have to incorportate different gas clouds with different relative velocities during planetary formation.