This article is from the General Cat Care FAQ, posted to rec.pets.cats newsgroup. Maintained by Cindy Tittle Moore with numerous contributions by others.
Most cats will love playing with you. There is the usual string or ball chasing; a few will even retrieve thrown items. "Hide and seek" and "Peekaboo" are also popular. Cats commonly display interest by dilating their pupils; look for this to see what catches its attention.
Try a small pencil flashlight or a small laser light for a game of "flashlight tag". Cats love to chase the light across the floor, over furniture and up walls. The lower-wattage laser pointers (0.1mW or less) are quite safe for something like this. It would take many days of non-stop direct exposure to the beam to even *start* to do any damage to eyes.
Cats will often display behavior commonly called "elevenses," since it seems to occur most often around 11PM. This consists of the cat's eyes dilating, its tail poofing out, and alternating between hopping sideways and racing all over the house. Your cat wants to play. Take it up on the challenge. Chase after it, play hide and seek. This can also be useful; playing with a cat just before bedtime reduces the chances of your cat wanting to play with you at 3AM.
In general, cats perversely favor the cheap homemade toy over the expensive supermarket toy. Toys commonly mentioned foil or paper balls, superballs, little plastic rings from milk jugs, ornaments on christmas trees, pencils, paper bags, cardboard boxes, Q-tips, cat dancers ... the list is nearly infinite.
A new "cat toy" seems to be the production of videotapes for your furry feline. Tapes of birds and mice complete with intriguing noises have kept several reader's cats entranced. If your cat seems to like watching TV (some do), this might be fun for your cat. Don't give it access to your remote, though.
Take sensible precautions with toys that can injure the cat: avoid toys small enough to be swallowed or choked on; avoid toys with loose or potentially sharp parts; avoid toys that can strangulate the cat or shred the intestines if swallowed (including string and rubber bands). Put strings away when you are not at home.
You can order a large catnip tree from Felix (1-800-24-Felix), especially if you cannot make one on your own because of lack of skill, time, or workspace. Cats especially enjoy being able to climb up and down these structures. Big ones should be bolted to the wall for stability. Most pet stores sell these things. Expect to pay no more than US$100 for a good sized one. Look for sturdiness and balance.
Sisal has been recommended over carpet for a scratching post cover. Cats seem to like the texture better, and it helps avoid confusion over which carpet is the "right" carpet to scratch.
You can also buy rectangular chunks of catnip-treated corrugated cardboard scratching 'posts', available at pet supply stores for about US$8 each. They can be either hung from a door, tacked to a wall or just laid flat on the ground. You might have to "show" them how to use them. Most cats love the texture of the cardboard (as well as the 'nip).
You might try used automobile tires placed upright and tied securely. Cats that like horizontal scratching posts jump up on it and scratch and cats that like vertical scratching posts stretch up and scratch. The tires can be bare or themselves covered with scratching material. In addition, cats have fun going through and around the tire.
Other readers have reported using wooden boards wrapped several times around with burlap. The burlap can be replaced as it is shredded.