Short answer: Yes, you can, but not without some hassle and a lot of harddisk space.
Blu-Ray discs can be read by some programs if you have the libbluray library installed. Check your favorite media players' websites and documentation for more details on that.
However, most commercial BDs have a content scrambling/encryption system applied that requires a registered media player to work. Check Wikipedia for more details. Obviously, open-source players won't be able to register with the authorities concerned because that would expose the encryption keys, so there are currently none (AFAIK) that can play commercial BDs. All you'll be able to play is non-commercial BDs. BD-ROMs probably wouldn't be encrypted, so those you can use.
There are some programs that can read the data from commercial (i.e. encrypted) BDs directly, decrypt it if the disc is older than half a year or so, and convert the result to a video file that you can play from your harddisk afterwards. This works because BD encryption keys are continuously being cracked. The movie industry will change the keys on newly produced discs, but of course they can't rewrite discs already released. One such program that I know of is called MakeMKV, but there are others. Search the web for them if you want.