Virtualdub can do this (it is free). You would just select starting frame, then ending frame, and ctrl + x to cut the selection. When you are finished with all the cuts, you just export to avi. (you can convert the avi to any other format, like mp4, with a great, also free tool, like Mediacoder is. ). In some cases (the person will be speaking saying an important comment, you might wish to keep that one, and cut surrounding silence.)
You can even export as well animated gifs, filmstrips, or image sequences. As for import, you can import avis (again, you can use mediacoder for conversions) , image sequences (obviously properly numbered) or a collection of other movie formats. You can also export the raw audio, in case the audio needed to be cut abruptly, and edit in a software like Audacity,(free) where you can make fades in-out, etc, and then...Import later the audio track into multitrack video sofwtares (virtualdub is not). These softwares allow multiple video tracks, edit sound track, add video overlays easily, etc... I'd strongly recommend use some very few bucks in Sony Vegas,platinum works great for me, but possibly could do with the other one too, it is amazing. It's great to do those tasks you wont do with Virtualdub. (fabulous for raw cuts , anyway.)
Note: You don't need the Sony Vegas extra power, nor audio editing like Audacity's, if just want to crop parts, Virtualdub is enough.
Last and important note. While saving to avi, or converting (with mediacoder) the avi exported from Virtualdub, is key thing to use good codecs. These are installed in your system, are like compression modes for video. A format can use several codecs. So, you can save in avi format, but using camstudio codec (great for lossless editing while keeping file small). Or mp4 format, but saving in .h264 codec (using, for example, Mediacoder converter)