Ah! Finally someone who would appreciate the utility of such software besides myself.
The good news here is that it's all freeware. I bought several video editing software (4 or 5?), but the one I use is Virtualdub. The "stabilizing" filter is a plug-in called Deshaker, written by another guy, which runs under Virtualdub.
These guys write wonderful freeware that beats the pants off commercial software. Download them and spend many hours having fun like I did. The best things in life are free (like this forum).
Note: Whatever PC you are using, you will wish you have a faster one. These are CPU intensive software, despite being written partly in assembly language for speed (these guys are that good).