Ask yourself some general questions when looking at a used machine. Does it appear to have been well-maintained? Is it reasonably clean? Ask the seller to check the oil, and other applicable fluids or lubrication points. This will show you if the machine is currently in good condition. Also if a seller is not familiar enough with the machine to do this for you, he probably didn't perform routine maintenance. Ask for a "test drive." Evaluate how easily it starts, how comfortable it is for you to use, and how efficient the machine is for the type of job you have at home. Ask where you can take the machine for servicing, if necessary. This applies for new or used equipment, since not all places that sell garden equipment service what they sell. For specific tools, new or used, look for the following characteristics. Chipper/shredders. Consider maneuverability, balance, the clutch system, and ease of feeding material into it. You don't want to lift heavy materials or shovel loads over your head to use the machine. A grate to regulate the size of material as it comes out will eliminate running material through twice.
Rototillers. Rear-tine machines are generally the easiest for most people to operate. After test driving, does the machine leave a well-prepared, fluffy seed-bed?
Lawn mowers. Variable speed drive offers a choice of working conditions, which is valuable because grass and mowing conditions vary. Opt for a mulching type of lawn mower if possible. Not only are they the most efficient, but they also are the most environmentally responsible. If looking at self-propelled mowers, try to find one with at least a five-horsepower motor. For the difference in price, it will last a lot longer than a smaller engine. For machines with baggers, test the bag. Look for ease of handling, removing, and emptying when full. If your yard is fairly even and free of debris, consider a push-reel mower.
String Trimmers. Try one long enough to determine if it is comfortable for you to use. Is it well balanced or too heavy? Correctly match the machine to your job at home. For grass edging, a small, curve-shaft trimmer should suffice. A mid-size trimmer will be more effective for weeds, but clearing the back forty acres may require a heavy-duty, two-handled model.
Hedge Trimmers. Make sure the tool can be sharpened; many cannot. Consider how much it weighs. Is it too heavy for you to operate comfortably for extended periods of time?
Leaf Blowers. Air speed and the volume of air the machine moves are equally important. Check the consistency of the sweep. Does it move material equally well at the edges and the center? If the machine has a vacuum attachment make sure material is not forced back through the fan blades.
The gamble of buying used equipment is you may just be getting someone else's headache. Without being too intrusive, you may want to approach this by asking if the seller still plans to garden. If so, then either the equipment no longer suits his purposes, or the gardener's sick of it! 
If you have a Sunday newspaper handy, check the classified ads for used gardening equipment. From chippers to string trimmers, used equipment is a respectable market. Also look at yard sales and estate sales for used equipment. 