Remove rounded nuts/bolts from wheel on old bike
If the nuts are rounded they're stuffed.  You want to remove the nuts but not damage other things, like axles.

I'll assume you're talking about axle nuts, but the same ideas apply to all nuts, bolts, and even screws to some extent.

So your nuts look something like this:




Clean the flats up with a file.  Use a medium flat file and smooth off the lumps of deformed metal in the corners.  Keep the file parallel to the flats and take your time. 
Get the right-sized tool.  An axle nut is often 14mm, but that's not quite 9/16" of an inch.  So try the near-size tools.  They should go on snugly and have minimal play
Use a 6 or 12 point socket, or a ring spanner.  There's even specialist axle nut spanners as pictured which work quite well.     .Do NOT use an adjustable crescent!
Leverage - get a length of pipe and slip it over your socket driver handle. 50cm to 1metre should be ample leverage.  Any more than that and you risk damaging the tool.
If that's not helping then stop here, and get some penetrant oil like PB Rust Blaster, or CRC or anything that will soak in and help break up corrosion.  It could be the nuts have rounded off because they're simply on really well.  Also look for pins or any other secondary retainers.  My landy uses tab washers, which are designed to be folded over nuts to hold them from vibrating loose.


So all the easy fixes have failed.  You're going to have to get brutal and your nuts probably won't survive the later options.


Vise Grips or a Pair of Stiltsons, aka a pipe wrench.     
Leverage is your friend, but watch the slip-zone should something give way.
Cold chisel works well on larger diameter things, but small nuts not so much.  I'd not bother with this.  The shock of hammering may upset your bearing cones and cups inside the hub and even the headset takes abuse.
If you have one, try cracking the nut in two with a nut splitter 
Finally you can get a small 3" or 4" grinder with a cut-off wheel and thin down the nut.  The danger here is slipping and damaging the axle, or the wheel hub, or yourself.  Plus there's hot spitty sparks which can set fire to lubes and oils and cloths and anything.   A dremel tool with a 1" cutoff wheel might work, but the wheels tend to shatter quickly which is also expensive.  
If you can't cut the nut off, then consider cutting the whole axle off.  The nuts pictured above would work well because the flange is a good guide of where to cut.  Once the top part of the nut is off, the flange may slide right off at best, or its only got a couple of threads to undo and you have more leverage.  A new axle is absolutely needed because it will be too short, and will have overheated changing its hardness.


Sometimes heat can help, but its also able to cause worse damage.  A steel fork should be fine, but its very easy to overheat aluminium.  Carbon fibre will melt badly or worse it might overheat, loose strength, but look undamaged.  This is the worst case, so only apply heat if your fork is steel, and there are no plastic parts in the area.

You can also use cold, sometimes, to "shrink" metals and break things loose.  I've found that carefully-applied heat to be much more useful.

Once you get the wheel nuts off, consider replacing the axle and nuts anyway.  A new axle with wheel nuts, two cones, and lock nuts shouldn't be too expensive.