DVD ripping tools are usually a contentious topic seeing as they can be used in ways that violate copyright laws. However, there are a number of reasons why a user would want to transfer a legally owned DVD to their computers - perhaps to avoid lugging around the discs while traveling or simply as a precaution in case they get scratched into oblivion. Enter HandBrake, a cross-platform tool that'll get the job done easily and for free.
First off however you should know that HandBrake is about video conversion, not stripping copy protection, so you won't be able to rip most commercial DVDs - at least not without a third party tool like AnyDVD or the like anyways. It also supports DVD decryption through VLC on OS X and libdvdcss on Linux. Legal issues aside, converting videos with HandBrake is a fairly simple process: just select a source, then set up the output file and encoding settings (you can choose from a number of presets). Moreover, as of version 0.9.3, HandBrake is not just for DVDs any more as it can now take practically any type of video as a source.
This open source application is well worth a look if you want your purchased DVDs available on your laptop, iPhone or other similar device. You can download it here or check more details, such as a list of features and walkthrough information, on their website.