HandBrake is an open-source, GPL-licensed, multiplatform, multithreaded DVD to MPEG-4 converter, available for MacOS X, Linux and Windows.

Supported sources:

Any DVD-like source: VIDEO_TS folder, DVD image or real DVD (encrypted or unencrypted, but protection methods other than CSS are not supported and must be handled externally with third-party software), and some .VOB and .TS files
PAL or NTSC
AC-3, DTS, LPCM or MPEG audio tracks

Outputs:

File format: MP4, MKV, AVI or OGM
Video: MPEG-4 or H.264 (1 or 2 passes or constant quantizer/rate encoding)
Audio: AAC, MP3, Vorbis or AC-3 pass-through (supports encoding of several audio tracks)

Misc features:

Chapter selection
Basic subtitle support (burned into the picture)
Integrated bitrate calculator
Picture deinterlacing, cropping and scaling
Grayscale encoding