AM
I have worked 10m AM a few times and have found it to be very interesting.  The improved audio quality over SSB is attractive, though it requires a better band opening.

FM
The most common FM work is done on the local repeaters, but some time has been spent on 10m FM (both repeaters and simplex).  Generally the contacts have been Stateside, but rare DX has also appeared.  The beauty of FM is that when it's open, the other station sounds like they are only across town.

PSK 31
I was newly introduced to this mode this past winter.  After constructing an interface kit to go between the PC and the radio, downloading Digi-pan (shareware), and setting up the soundcard on the PC I was ready to go -- all for $25!  I have found PSK to be like fishing in a barrel -- very easy to make contacts with minimal power.  With the waterfall display of the software, you can see all the stations on at one time, so it is much easier to make contacts.  This mode is truly a marvel!

Satellite
Although I have tried to work via satellites, I have been unsuccessful so far.  I have been able to receive signals from AO-27 and RS-13, but have not had the right setup to make an official contact yet.  This is one of my next goals!

Mobile
My main rig is the Icom 706, and this past fall I got our Dodge Grand Caravan outfitted for mobile operation.  The radio is powered from the van's battery, with 10 gauge wire running to the rear of the van and then up through the back bumper, under the carpet and stowed behind the jack cover.  The faceplate is mounted to a bracket that attaches to the dash with velcro.  The antenna is a Hamstick, with a quick-coupler to mount it on a homebrew bracket that bolts to the frame and angles toward the corner of the bumper.  The angle allows the back door to swing open, missing the antenna.  Three contacts have been made on 17m using this setup so far, and good signal reports were received each time.  This is a great way to pass the time on a long trip!!