pops117: The last time I tried DVDShrink had no problem with protected DVDs. The only thing it was unable to backup were badly scratched discs, but neither could it be recovered with any other software so...
DVDShrink hasn't been updated since 2004, so some discs using newer forms of protection can't be copied by it; if much of your collection was released prior to that or doesn't use incompatible protection you won't have many problems, of course.
I've had good results using DVDShrink to rip from damaged discs, so it's well worth a try if only as a last resort before throwing the disc away. ImgBurn and the like can achieve the same result but refuses to copy from protected movie DVDs; for all other disc types (including game DVDs with DRM) it can get the job done.