That's called rippling. And, as I say in my book, there are a couple of ways to keep it from happening (since, most of the time, you do want it to happen).
Just hold down the Ctrl key (or the Cmd key on a Mac) when you add or move your clips and the other clips will remain in position.
To remove a clip without rippling the rest of the timeline, select the clip and press the Delete key) next to the End key rather than deleting with the Backspace key.
And, one little tip to add to Steve's suggestions: if you do Delete material, and do NOT Ripple Delete, you will have a gap. You will not want any gaps in your Video, so you will either want to close the gap, or fill it with Black Video (from the New Icon).
Thanks! Both very helpful tips and much appreciated. The Ctrl key worked. I much prefer telling the software when and when not to close gaps and ripple rather than have it decide for me. Currently, I am working on a music video so I am syncing the video to the music and need it to stay in place. I can see how that would not be such an issue if it were the other way around.
Not that I can afford it now, but do you know if the Pro CS5.5 version has the same auto-ripple feature?
Actually, PrPro is just the opposite. You use the Ctrl key TO Ripple Edit. PrE's designers felt that Ripple Editing was going to be more common for its user-base, so made Ripple Editing the default. As I work with both programs, I often have to pinch myself, to remind me which I am using, as this function is just reversed.