Try Goo Gone. It works well. However, as with any product, try it in a inconspicuous place first.

Goo Gone is safe and easy. Another alternative is Stain Devils #1 by Carbona - its made up predominately of Ethanol, so is flammable but it works pretty good on adhesives. Its marketed for clothing gum, glue removal.

Don't do it!! I usually value a game more if I know it's history. I was thrilled to get this old Haunted House - and knowing exatly where it was routed back in the 80's is pretty cool IMHO.
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Heat gun works wonders on stickers and labels.
Use caution of course...

That baby's been around!!

Paper stickers come off fairly easy with peanut butter. Put a fair amount on the sticker and let sit overnight. Then wipe it off, the peanut butter will remove most of the sticker the first time, usually comes off easy after sitting overnight.

You can do it a second time with less if it doesnt come all come off. Never had damage to the paint underneath the few times I have done that.

Not sure it will work with metallic type stickers? Only removed paper ones with this method.