The baseball bat is a common melee weapon found in the Wasteland. The United States was stereotyped a patriotic country, so it's very logical to find them everywhere. While useful for close combat with raiders, they are not particularly effective against the more durable foes found throughout the Wasteland.
All things considered, Fallout 3's baseball bat is a decent melee weapon for early use and helps to preserve ammunition when starting out in the wasteland. Later, much more powerful melee weapons become available, such as the Ripper and Shishkebab.
The following is based on Fallout 3 cut content and has not been confirmed by canon sources.
Curse Breaker - A unique baseball bat that was cut from the base game. If it is equipped on the PC version, it makes your character disappear. This does not help with sneaking.
Excalibat - Another cut baseball bat in the base game. The name "Excalibat" is a nod to the FPS Rise of the Triad: Dark War weapon of the same name.
End of information based on Fallout 3 cut content.
Vault 101 in the beginning of Escape!. It is on a table with the BB gun and 50 BB pellets.
The bat is branded on one side with a machine-caligraphed "B" in an ovoid shape. Beneath the logo are the words "Since 1879," suggesting the bat's manufacturer has been producing sporting goods since the 19th century.