How often do you get to "play with" scientific instruments? I tend to learn and understand a subject to a much deeper extent if I am able to play around/experiment/mess with something that demonstrates the principles. 

I'm starting a Neuroscience PhD program in the fall and would like to know how I could maximize the opportunities to experiment with various equipment at the university. I'm interested in working with things like fMRI, MEG, EEG, electron-microscopes, and supercomputers.

How easy is it to informally play with these types of equipment when they might be sitting idle?

Note: I'm looking to do this safely without any intent to damage the equipment. Primarily, I'm looking to replicate the findings of classic experiments and discover aspects that didn't make it into the published papers.
It depends to a large degree on who owns them.

If it's your lab group, and your supervisor's happy enough, you can probably use them whenever you like. 

If they're owned by the department/division/etc then there's likely to be a formal booking system. Once you've booked a slot, though, I'd imagine you can do whatever work you like on them.

Provisos in this are cost and safety. 

Cost, because some of the stuff you're talking about is pretty pricey. An fMRI session can be charged at over $400 dollars per hour. 

Safety applies to you and the equipment. You may well intend to be safe and not damage the equipment, but that can be easier said than done. As such, you're never going to be allowed to use certain items without having gone through the necessary training - so you'll have to convince your supervisor that doing such training is a good use of your time/funding. 

So in your lab, play around time will I suspect be limited, save on equipment you use daily. But if you must get your hands on a piece of kit, fear not, for there are workshops and courses you can attend! These often occur in conjunction with a conference/meeting/etc of some kind, where a sponsoring vendor will kindly 'donate' a piece of equipment (in the hope you'll buy the same brand later down the road) and as a group you get the opportunity to spend a while using it under the company representative's watchful eye. Keep an eye out for these, and try to arrange to publish a paper in the conference, or give a talk in the meeting, and I'm sure you'll be given the funding to go.