Fundamentals

Below is a list of bat care tips that will help you keep your bat in the best condition possible for the longest time possible. Although each manufacturer may offer slightly different information, the basic principles apply to all bats.
You should always note where and when the bat was purchased for the sake of keeping track of the warranty. This is important if you want to replace the bat at a later date. Most bats are not designed for use with the heavy Beep Baseball, so it is essential that you give it proper care and inspect it on a regular basis.

Inspection

Routinely check your bat for any damage.
Even a small scratch and/or dent can compromise the durability and integrity of the bat. Moving your fingers around the surface of the bat is the best way to locate minor defects. It is useful to keep the bat surface clean and familiarize yourself with the way that the surface feels so that minor defects can be readily identified.

Roll the bat on a smooth, flat surface and look for signs of warping or denting. This is a particularly important step before you use any bat for the first time or after it has been stored for a long period.

Limit the bat to individual use.
By knowing how your bat has been used, you can appropriately monitor its condition. It will also last longer and ensure that the bat you feel most comfortable using is always available.

Do not use in temperatures below 60 degrees Fahrenheit (16 degrees Celcius).
Playing in weather below 60 degrees Fahrenheit can be very harmful to a bat. In lower temperatures, the density of some older bats can change, making the bat more prone to dents and cracks. More significantly, lower temperatures cause both softballs and baseballs to become harder. A harder ball can contribute to major bat damage.

Do not physically alter the bat in any manner.
Altering a bat will void its warranty and potentially its durability. Alterations include, but are not limited to:

Use of Items With Your Bat

Use regulation leather covered, baseball, softballs and Beep Baseballs, NOT rubber cage balls.
Rubber dimple balls used in practice and batting cages can seriously impair the finish of the bat.
The use of bat "sleeves" with cage balls also may not protect your bat. In most cases, hitting cage balls will void your manufacturer's warranty.

Do not hit waterlogged balls
Using a waterlogged ball will further increase the weight of the ball and cause unnecessary stress to the bat.

Preventive Measures

Do not clean cleats with the bat
Avoid cleaning your cleats by tapping your bat against them. This is not good for your bat nor your cleats. While this action is especially a concern if your cleats have metal bottoms, it should be avoided even if you are wearing plastic or rubber cleats.

Rotate your metal bat 1/4 turn each swing.
Rotating your bat slightly after each swing ensures that you are breaking in the entire circumference of the bat barrel. It also makes certain that you aren't over exerting or wearing down one area of the bat more than another.

Do not store the bat in extremely hot or cold temperature areas.
Avoid storing your bat in extremely hot or cold environments.
Take your bat to an indoor, climate controlled location after each time out.
Do not leave it in a car or garage.
If you are storing multiple bats together, it is recommended that they are covered with a bat sleeve so they do not clash together.

Keep the bat away from damp areas.
Try not to expose it to wet substances and/or surfaces. If the bat does get wet, dry it immediately.

Wood bats should be stored with the knob side up.
Lean the bat up against a corner in as straight up and down a position as you can get. An out-of-the-way corner in your room or a closet are good suggestions.

Cleaning and Caring for Your Bat

Cleaning
Here are some suggestions for both metal and wood bats, but you should always refer to the manufacturer's instructions for your bat.

Metal Bats
To protect the finish of your metal bat, clean it when covered with dirt or grime.
The best way to clean your bat is with a soft wash cloth and mild soap and warm water.
Most manufacturers will warn that the use of solvents or ammonia based products can damage the finish.

Wood Bats
Wipe your bat with alcohol every day, especially if the handle is immersed in pine tar or other substance.
Alcohol cleans the bat and prevents tar and dirt buildup
If your bat has a color or clear coat, use Windex Multi-Surface Vinegar (or whatever the manufacturer suggests) on a dry lint-free cloth if you want to clean off the ball marks.
Spray the Windex Multi-Surface Vinegar on the cloth then wipe the marks in the same direction as the grain of the wood.
Immediately take another clean lint-free cloth and wipe off the bat until dry.
This method can be repeated as needed.
While there is no perfect solution that will completely remove all marks without the risk of marring the finish, this method has proven the best in testing to minimize that risk.
Once the ball marks are out, take a spray can of clear semi-gloss polyurethane and lightly spray the barrel of your wooden bat.
Hang the bat from the knob on the handle and let the bat dry.
By doing this, will be able to see how you are hitting the ball from game to game.

For unfinished, natural, wood bats
You may try a very fine grit sandpaper (200 grit or higher) to lightly sand the ball marks, moving the sand paper in the direction of the grain of the wood.
Avoid going over engraved areas and any logo.

Resources

Caring for your Phoenix Wood Bat
Caring for your Baseball or Softball Bats
JustBats Resource guide for your Bats