# Removing BOM from all text files in current directory:
sed -i '1 s/^\xef\xbb\xbf//' *.txt
On FreeBSD:
sed -i .bak '1 s/^\xef\xbb\xbf//' *.txt
Advantage of using GNU or FreeBSD sed: the -i parameter means "in place", and will update files without the need for redirections or weird tricks.
On Mac:
This awk solution in another answer works, but the sed command above does not work. At least on Mac (Sierra) sed documentation does not mention supporting hexadecimal escaping ala \xef.
A similar trick can be achieved with any program by piping to the sponge tool from moreutils:
I know the question was directed at unix/linux, thought it would be worth to mention a good option for the unix-challenged (on windows, with a UI).
I ran into the same issue on a WordPress project (BOM was causing problems with rss feed and page validation) and I had to look into all the files in a quite big directory tree to find the one that was with BOM. Found an application called Replace Pioneer and in it:
Batch Runner -> Search (to find all the files in the subfolders) -> Replace Template -> Binary remove BOM (there is a ready made search and replace template for this).
It was not the most elegant solution and it did require installing a program, which is a downside. But once I found out what was going around me, it worked like a charm (and found 3 files out of about 2300 that were with BOM).