What formats are you talking about?
I use adobe premiere pro to edit my game footage (very much not free though). I know other coaches use similar programs. It says it can import:
.ai .eps .aif .wmv .wma .asf .bmp .dib .rle .avi .dlx .flm .mp3 .mpeg .mpe .mpg .m2v .mpa .gif .jpg .jpe .jfif .png .ico .pcx .psd .pic .pct .pict .mov .tga .icb .vst .vda .tif .tiff .prtl .wav .plb .psq .ptl .ppj .prproj
granted most of these are not video formats (pictures titles etc) but some are. If I tried to import things like .vob I googled .vob to .avi and got a free program on my last computer to make .avi files and do it that way but can't remember the name of the program as i have a new computer and have not had the need since.
If you are doing a lot of editing though that is painfull because you must convert all files and then edit. Time consuming, but if you only have a few files to do its not that bad, but i wouldn't do it for things like a whole game.
What are you editing and what file types are we talking? I think the easiest way would be to work out exactly what file types you will be using then search for a program that can import them, maybe someone with more computer skills can confirm? I by no means pretend to be a computer geek, but that is how I have done it in the past. Hope that helps.