Yes, I believe that the principle still applies today. Implementing it, however, can be difficult. One difficulty, of course, is that we just don't want to.
In that respect, there's nothing new under the sun.
Another way that it's difficult is that there is a conglomeration of issues that overlap: Turning the other cheek, forgiveness, justice, preventing harm to others, legal process... etc.
An example: Some years ago, I was the target of an online stalker. He sent me sexually threatening anonymous messages -- well, not really anonymous, because he had disguised them to look like they came from people I knew (he was an expert hacker apparently). It became clear that he knew the details of my life and was watching me daily. Well, it took a few weeks, but they traced the messages; it turned out it was the guy who lived right across the hall from me. I picked up the pieces and got back to life as usual (I had moved to a separate location for safety reasons). The one thing I did was tell the police that yes, I would like to press criminal charges. Well, I got thoroughly attacked by a group of other Christians who accused me of being "unforgiving" because I wished this man to be answerable for what he did. They interpreted "turn the other cheek" to mean "let him get away with it;" I interpreted "turn the other cheek" to mean "allow the law to do its job but don't seek your own vengeance." It was a matter of how to interpret and apply this principle, and we differed significantly. (And let me say that, oh yeah, this was a
great time period for me to be attacked by fellow Christians!
)