Plastic Furniture: We like this tip we read on the Sun Herald:Wash plastic furniture with three tablespoons of powdered laundry detergent (or oxygenated bleach such as OxyClean) mixed in a gallon of warm water. You can try using car wax to seal plastic, it'll make water bead off of it. Just make sure you've wiped the extra off before anyone sits in it.
If it still isn't clean, they do make spraypaint for plastic, and you might want to consider a fresh coat of paint.
Keep in mind that plastic can deteriorate in the sun so there's a chance that even once you've cleaned it, they might just be too old. Consider replacing them with more eco friendly pieces.
Wood Furniture: If you haven't covered it or stored it inside somewhere, then it's probably faded and/or dirty. Try some mild soap and a sponge with a scrubby green side to get some of the grime off. If it's teak, make sure you've dried it thoroughly and then add some teak oil to add shine and depth to the grain of the wood.
Umbrellas: These can be washed, normally with laundry detergent, though we read a pretty smart account of using one of those do it yourself car washes to get it super clean. As always, follow the directions on the fabric and always allow to dry completely otherwise it'll mildew.
Cushions: Your best bet is to mix up a solution of 1 teaspoon dishwashing detergent
1 quart warm water and 1 tablespoon borax and let it sit on the fabric for a couple of minutes. Then wipe, rinse (a hose is useful) and allow to dry in the sun. Once it's dry try spraying it with scotchgard to protect it through the summer.
Aluminum: Use diluted dishwasher soap and scrub.
Iron: Obviously this can rust and if it has, you really ought to sand it down and seal it with touch up paint or wax. To clean it, use diluted dishwasher soap and make sure to dry well.
Concrete: It's been more popular lately to have poured slabs of furniture in the garden. if this is you, you get to rent a pressure washer and power wash all the grime off (we're jealous!).
Have we missed anything? Do you have a great shortcut for any of these?