Is it possible to implement an MVC concept with or without ASP.net MVC for SharePoint 2013?
As Daniel says, if you are building an App, Provider Hosted or Auto Hosted which both have components that run off your SP2013 server, that remote part can be MVC (e.g. ASP.Net MVC4 or 5).
If what you want to use is the concept, then yes you can definitely do that too. You can do SP2010 webparts (farm solutions) with a MV(C/VM) architecture, if you're really into it. We do most of ours like that, it's more upfront work but once your base architecture is laid out it works pretty well.
As I've understood it, it is possible to implement MVC into your SP2013 Apps but not into any SharePoint solutions or the like.