(Reprinted from Jacci Howard Bear @ About.com)

Strip-Cut

Strip-cut shredders, also known as straight-cut or spaghetti-cut, slice the paper into long, thin strips. Strip-cut shredders generally handle a higher volume of paper with lower maintenance requirements. Shred size may vary from 1/8 to 1/2 inch. Narrower strips provide better security. Because the strips don't compress well, you'll need a larger basket (or more frequent emptying).

Cross-Cut

Cross-cut shredders provide more security by cutting paper vertically and horizontally into confetti-like pieces. The shredded paper compresses better so the basket holds more cut paper. The trade-off is these shredders may require more maintenance and generally cost more. With patience someone could reconstruct any shredded document. Cross-cut shredders just make the job a lot more tedious. Volume/Capacity

Further Info

It's easy to burn out a shredder by overworking it. For low-volume users, personal shredders designed for 100-150 sheets per day are fine. For higher volume look beyond personal shredders. A shred capacity of at least 4-5 sheets is best unless you really want to spend time feeding in paper one piece at a time. In real-world use, most shredders do best at 1-2 sheets less than their stated specs. Throat
The opening where you feed the paper into the shredder needs to be large enough to accommodate the size of paper you typically shred. An 8.75 or 9 inch throat handles unfolded letter size paper nicely. A smaller throat size requires folding the paper but if most of your shredding is of credit card or ATM receipts, it works fine. Extra Features
Shredders come with various combinations of features. With Automatic start/stop the shredder detects the presence of paper. Some shredders provide a light or buzzer to alert you to paper jams or a full shredder basket. Reverse Feed is useful for helping to clear out paper jams. A clear basket or window also helps you see when the basket needs emptying. Integrated Units
Shredders with built-in baskets or racks for plastic bags generally cost a bit more than the stand-alone versions. These shredders come in a variety of shapes and sizes. Some units might include an extra opening for inserting paper that doesn't need shredding or a see-through window to check the paper level. The main drawback is that you are tied into using a specific size of basket.

Stand-alone Units

This type of paper shredder fits on most standard size wastebaskets. Expandable sides allow you to adjust it for different width baskets. These are often the least expensive units and can usually be purchased for under $60US. For the greatest flexibility, look for a unit that fits both round and rectangular baskets of varying sizes. Supplies
Some manufacturers recommend using shredder bags. These bags come sized to the dimensions of specific models, although ordinary trash bags may work fine. To keep a shredder operating at peak efficiency the blades should be oiled regularly with specially formulated shredder oil. This oil lubricates without leaving residue on the cutters that can attract paper dust and lead to clogged cutters.