Legality depends on what you do with it.
Lets' start with copyright. It's exactly as the name implies; it's the right to copy. Thus studios and developers want to enforce their right to determine the copies being made. So, when a copy is made without the copyright holders permission, that's an infringement on the copyright. There is more to it but this is the basic premise.
The thing is, when we purchase a movie, CD, video game, we are not purchasing the copyrighted work. We are purchasing a license to use the media the copyright holder has released. The tangible media is the representation of license. Media = License/No media = no license.
So making a copy of the DVD/Blu-ray can plainly be seen as an infringement on copyright. BUT, as others have mentioned, there is a "Fair Use" exception. There are 4 factors to Fair Use:
(1) the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
(2) the nature of the copyrighted work;
(3) the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
(4) the effect of the use upon the potential market for or value of the copyrighted work.
So to go one by one:
(1) the purpose and character of the use is for personal back up; (Good factor)
(2) the nature of the copyrighted work - in this case movie (Neutral factor)
(3) the amount and substantiality of the portion used is the whole thing (Bad factor)
(4) the effect of the use upon the potential market for or value of the copyrighted work brings us to the stick point.
Studios, developers and artists say the impact on the market is that is lessened. However, the
people claiming Fair Use would say there is no impact as they already purchased and will not be distributing (the last part is key). So if the court finds that the market is not impacted or marginally impacted, there may would a Fair Use exception.
In fact, there are 2 cases that allowed copying: [Sony Corporation of America v. Universal City Studios, Inc.] (a.k.a the Betamax case) and [Recording Industry ***'n of America v. Diamond Multimedia Systems, Inc.]. The U.S. Supreme Court developed the theory of "time shifting" and "space shifting" through these cases respectively. In the Sony case, the Court basically said that the personal user was shifting when they watch the TV show recorded on the Betamax. In the Diamond case, the personal user was shifting the space from computer to their MP3 player.
However, the counter point comes from [A&M Records, Inc. v. Napster, Inc.] and [Metro-Goldwyn-Mayer Studios Inc. v. Grokster, Ltd.]. The users argued that this was sharing like making a mix CD to be given to a friend. The U.S. Supreme Court did not buy the argument and saw the P2P programs were for active distribution (Grokster even advertised that you can get free movies). Thus both were shut down as infringements of copyright with no Fair Use exception.
Lastly, Lee Koo did mention the Digital Millennium Copyright Act (DMCA). He is also correct in saying that it is illegal to circumvent copyright protections. Thus, if you made a straight out bit for bit (b4b) copy, this would NOT be illegal. However, a b4b probably won't work on a computer which may mean you have to change it. If you had to use software to overcome a block, DMCA says it illegal. Otherwise, you may be okay based on the Sony case and the Diamond case.
Interestingly, it is LEGAL to reverse engineer or decrypt protections for EDUCATIONAL PURPOSES ONLY.
So going back to the main point, if it is a simple copy and you are using the copy strictly for personal use, it is probably going to be LEGAL. If you had to overcome any sort of protections (this is generally found as cracks for video games) it is most likely ILLEGAL.
As a final word, if you buy the multi-disc Blu-rays, usually, you are already paying for the license to make a digital copy and the studios generally make it easy to obtain the digital copy so you won't be tempted to use a program to hack the movie.
P.S. the reason I know all the above is I did a 40 page independent research paper regarding User's Rights to Digital Media.