.png file - Generally for web or screen use, and allows the logo to be placed on any background color.
.jpg file - Can be used for web, Powerpoint, or for printing something in a small size. If scaled larger, "jaggies" (anti-aliasing) may result. Because it is pixel-based, as a .jpg is saved and resaved it will suffer loss of resolution.
.tif file - Usually for high-resolution items intended for print.
.pdf file - A vector-based image (can be scaled without loss of resolution). T-shirt makers and commercial printers prefer .pdf files or .eps files.
.eps file - Can be used by most designers and graphics screen printers (T-shirts, bags).
A note about white logos: Reverse logos are not provided here, as you would not be able to see them unless they were on a colored background. Commercial printers will print in white (T-shirts, bags, hats) from your black image.