This is something I've had to really try to get used to and manage. The Olympus stabilization looks quite interesting but I'm put off on the lack of 1080P @ 24fps (I think the new OMD is 1080i @ 24fps). In particularly, I love using some of my prime lenses that have much larger apertures but no image stabilization. On handheld shots, I've read a lot about either using over the shoulder rigs or things like the Merlin Steadycam. Unfortunately, these are quite expensive and somewhat impractical for amateurs just shooting home video. Cheesycam.com have come up with much cheaper alternatives for steadicams (<$200) but again these steadicam's require a lot of skill and initial setup in terms of balancing weights on it. And it's one more thing to carry around.
I think the most practical option for amateurs may be Manfrotto Fluid Video Monopod W/Head. I have not used one but have seen wedding videographers and it seems to be a great mix of stability and portability. Having already spent money on a manfrotto carbon fiber tripod and video head, I've opted to get my investment out of this. For speed, I won't always spread the legs and will use it as a monopod. In addition, I've seen some videos on youtube that suggest holding the camera with the tripod in the air as the tripod creates the weight balance that helps stabilize video. I've actually found this does help somewhat as well. See the video below:
http://www.youtube.com/watch?v=JW6AWmqa8ZM&feature=related
Now if I don't use a tripod, my best bet is to just find something to lean onto or rest my elbows on. Finally, just make sure you shoot with your arms tightly pressed against your body and your camera up against your nose to add yet another point of stabilization. Hope that helps from someone that is very much a noob at this stuff.