A true EPS file, with vector art, is best. A true EPS file has all the artwork lines from the original creation of the logo. Most of the time, and EPS file will have this vector info embedded in it. An Illustrator (.ai) file will also likely have that info.
A PDF file will sometimes have vector info embedded. If you have a PDF, send it on, and we'll check it out.
A high resolution pixel file---JPEG, TIFF, PNG, BMP and PSD are pixel files, but whether they're high resolution or not depends on how they were saved. If their "file size" is in the 10k-20k range, it's not likely they're high enough resolution. In the 100k range, they might be OK. If they are 1MB or larger, they're very likely OK. Send us the one with the largest filesize, and we'll check it out. Or send several files, and we'll see which one is best.
Low resolution pixel files. JPEG's or GIF's that are in the 10-20k range are usually way too low resolution.
Word files (.doc) or Powerpoint (.ppt) files.