What happens if I get a grant for my PhD project but I decide to quit and start another PhD somewhere else? My PhD is self-funded and I probably change in 2016. Can I apply for a grant now and then change my PhD later? 

Does it legally or ethically force me to stay and finish the project? 

Or my Prof can hire another PhD student after me to continue working on that project?

UPDATE

Let's put it this way: I have a self funded position and everybody including my Prof know that I'll most probably leave next year but I want to get some money as long as I'm here (before changing). 

Can I apply for a for example 2-year research grant and quit after a year or it obligates me to stay and finish the project?
Of course you are not forced, nor obliged, to finish your current project.

But it might very well be that, depending on your grant conditions, you will have to pay back the grant money, fully or partially, when you do not finish the project.

Furthermore, it might be wise to try to keep being on good terms with your current professor and colleagues. This is most likely achieved by involving them in your decision and motivations (which you might already be doing, as you write in your question).