When you're dealing with DVD playback in a stand alone player (the one you hook up to your TV)
The file format is VOB and there are IFO files which instruct the player in which order and how to play them.
Most retail DVDs take up more than 4.4GB. Usually 5-6GB of space.
So if you want to back them up directly and essentially make a clone of the disk, you will need to purchase DVD+R DL media. The DL stands for dual layer, essentially there are two layers on the bottom of the disc. There are also double sided media, so each side of the disc can be written to. These are horrible and begging to be scratched in my opinion.
Most blank DVD media is single layer and can hold about 4.4GB of data. As you will have realised by now this is not large enough to store all the contents of your retail DVD.
Thus, DVDShrink has been recommended by a few earlier posters. It does exactly what it says and transcodes the movie to shrink it to fit to the single layer media (4.4GB). Inevitably there will be quality loss in this conversion process. DVDShrink is what is commonly known as a 1 click application. You essentially just click backup and it will automatically do the necessary processes for you.
It will produce .VOB files and and a couple of IFO files.
Just use Nero or another DVD burning suite to burn the files as "DVD-Video files".
Personally I have not used DVDShrink or 1-click applications for a number of years. For the most part you will not be able to notice quality degradation except in demanding scenes. This is because it uses a constant bit rate. E.g a scene where a house is on fire, some parts of the fire may look blurry and/or pixelated. Most people won't mind or notice them but I have a very keen eye and makes my viewing experience displeasing as quality always comes first for me.
Give DVDSHrink a try and see if you like it.
Sometimes DVDShrink will not work on it's own and you may need to rip the contents of the disc to your hard drive first of all. This can be done, as previously stated, using anydvd in the background. Alternatively you can use DVD Decrypter for most disks. Newer DRM on disks renders DVD Decrypter ineffective.
Try to use +R media because this will allow you to set the book-type. This is like a label or identifier to the DVD player on how it should treat the disk. DVD-R media's book-type cannot be set and remains as -R so some DVD players, most notably the cheaper ones have trouble playing these disks.
With +R disks you can set the book-type to +ROM so it will play without hassle on any DVD player (as long as the disk is of decent quality and not the cheapest thing you could find).
To set the book-type you will need to do it with the burning software you use.
Single layer blank media is quite inexpensive nowadays. They can be purchased from between 10-20p per disk.
www.svp.co.uk www.ukdvdr.co.uk www.diskdepot.co.uk.
If you want to make a 1:1 copy then you will need the DL media which is about 60-80p per disc.
I personally use Cinema Craft Encoder SP with DVD Rebuilder Pro. This is a very long process. Where DVDShrink may take between 10 and 20 minutes to complete the conversion, DVD Rebuilder will take hours depending on how many encode passes you set it to.
There are some very good guides here if you want to learn more
http://www.afterdawn.com/guides/