I had a need to merge 15 mp4 files recently and a simple tool for the job is Avidemux. Just open the first file and select Append from the File menu to select the next one. Repeat until all of your files have been added. The default encoding settings are copy for both video and audio so you shouldn't have to make any changes before saving the new file.

As with any encoding job it's always a good idea to test the output file. I have a new phone and for some reason the audio was getting messed up after the first clip. I've never experienced that problem in the past.

You would think that finding a good video encoding app would be easy. Solid command line tools like transcode, FFmpeg, and MEncoder do exist, but readily available graphical apps are hard to come by. Frustrated with the dedicated alternatives, I turned to Avidemux. It's known best as an easy to use video editor, but the controls also make it very easy to just transcode video.