Generally speaking, 220 volt 50 HZ devices will operate on 240 volt 60 HZ systems, with a few possible issues.
1) If there's an induction motor involved (washer, dryer, etc.), it'll run 20% faster. Current and heat-wise, the higher voltage and higher frequency will somewhat balance. I've connected quite a few 220 and 415 volt 50 HZ industrial motors to 208, 240, and 480 volt 60 HZ systems with very few problems.
2) If there's a universal motor involved (the kind with brushes, like a portable power tool, or kitchen appliance), it'll run about 5-10% faster. Current and heat will be slightly increased, but not to damaging levels. I have a bunch of 220 volt 50 HZ drills, saws, etc., that I run on 240 volts 60 HZ without problems.
3) If there's a transformer involved, frequency will make very little difference, but voltage of the output will rise by about 10%. Not a problem in most cases.
4) If there's a switching power supply involved (like a computer type), there's no difference at all.
The reason to not connect a standard receptacle to a non-standard voltage is because in your absence, there's an almost certain chance of someone plugging something standard into it, and destroying the device. Even if it were labelled, some nit-wit would likely figure 'Hey, it's 220, my (insert name of macho tool here) will be twice as strong now!! It actually will...... for about 1/2 a second!
There are receptacles and plugs available that are rated for 250 volts. They are the same physical size as the standard ones, but the prong configuration is different, so as to prevent sending the wrong voltage to anything. A 15 amp 250 volt receptacle and plug has the two power prongs horizontal instead of the standard vertical. They come in single or duplex, and fit standard boxes and use standard cover plates. When connected to a 15 amp two pole breaker, they're also completely code compliant. You'll most likely need to run a dedicated circuit from the panel though. Google nema 6-15 and look at some of the pictures, and you'll see the difference.
Another possibility, if the load is small enough, is a transformer to go from 120 to 240. If the load is more than a couple of amps, these get expensive though.
P.S. Like nap, Petey, and just about all the other pros, my advice is also based on code. It's not all that difficult to comply with, and it insures a reasonably safe installation.