"What do people use to convert .ts files into one MP4 file? I've downloaded a couple of TV shows in HD from the Internet and I am trying to piece them together into one MP4 for my iPhone."
Transport Stream (TS) is a standard format for transmission and storage of audio, video and data. Transport stream offers features for error correction for transportation over unreliable media, and is used in broadcast systems such as DVB and ATSC. Though the video is joyful, it is no so widely accepted by most popular devices like iPod, iPhone, iPad and PSP.
To play TS files on Mac, VLC media player is an ideal one to accomplish this task. It supports various audio and video formats (MPEG-1, MPEG-2, MPEG-4, DivX, MP3, ogg, ...) as well as DVDs, VCDs, and various streaming protocols and works well on Mac, linux and Windows.
To convert TS to MP4 on Mac, what you need is a Video Converter for Mac. It can convert TS to MP4, and other popular video formats like AVI, WMV, MP4, MPEG, MOV, FLV, MKV. Besides, you can extract audio from TS and convert to MP3, AAC, M4A audio formats. And the conversion can easily finished with a few clicks.
Note: If you are using Windows and want to convert TS to MP4, you can refer to Video Converter Ultimate for Windows.
Click "Add Files" to load TS files or directly drag them onto the interface.

You can select " MPEG-4 Movie (*.mp4)" from the drop-down list of "Format" and choose a proper destination folder for saving output files.

Tips: You can also adjust resolution, frame rate, encoder, bit rate, sample rate, and channels to optimize the output file for your device like iPod, iPhone, iPad and PSP.
(After finishing all necessary settings,) Click "Convert" button to start to convert TS to MP4 on Mac. You can also preview the converted video files and set the action after the conversion is completed.
After finishing the conversion, you can easily put the video to your iPod, iPhone, iPad or PSP and enjoy them anytime and anywhere.