VirtualDub, a free light video editing and batch encoding program can do this. Grab VirtualDub and then look in Video -> Filters (Ctrl+F). Click “Add” and look for “resize”. With this you can resize the video if you wish, and you’ll note at the bottom there are “framing options” wherein you can add your letterbox. You can either use raw pixels or if it’s easier, an aspect ratio. What’s best, is you can do this to multiple videos in a batch process. Go to file -> job control (f4) and a window will open wherein you can add as many videos to the job queue as you wish. Click edit and define your process directories (batch in/batch out), add your videos, and hit Start and it’ll encode (make sure to remember to select a codec so it’s not uncompressed!) and convert the videos one by one and you can just minimize the program while it’s running.