The Mac-Forums Community Guidelines (linked at the top of every forum) are very clear, we respect US law and court precedence when it comes to legality of activity.
Therefore to clarify:
You may not discuss breaking DVD or BluRay encryption, copying, or "ripping" commercial, copy-protected DVDs.
This includes DVDs or BluRays you own. Even if you own the DVD or BluRay, it is still technically illegal under the DMCA to break the encryption. While some may argue otherwise, until the law is rewritten or the US Supreme Court strikes it down, we will adhere to the current intent of the law.
You may discuss ripping or copying unprotected movies or homemade DVDs.
You may discuss ripping or copying tools in the context that they are used for legal purposes as outlined in this post.
I have some .avi files of a tv show that I want to burn on a DVD-R to watch on my Macbook and DVD player. Is it possible to burn multiple episodes on the same disc? Also, can anyone recommend me a good and free disc burning program?
No, the OP isn't talking about a multisession DVD, he's talking about having multiple video files - all .avi that the OP wants to burn to a DVD to play back on the OPs DVD player. If the OP doesn't have a DVD player that supports playing back video files stored on a DVD and only supports the DVD-Video format for DVDs, the OP will need some form of authoring application, whether it be: Burn, Toast, iDVD, DVDStudio Pro, MovieGate, etc.