A simpler approach (outputs to stdout, doesn't update the input file):
sed '$ s/.$//' somefile
$ is a Sed address that matches the last input line only, thus causing the following function call (s/.$//) to be executed on the last line only.
s/.$// replaces the last character on the (in this case last) line with an empty string; i.e., effectively removes the last char. (before the newline) on the line. . matches any character on the line, and following it with $ anchors the match to the end of the line; note how the use of $ in this regular expression is conceptually related, but technically distinct from the previous use of $ as a Sed address.
Example with stdin input (assumes Bash, Ksh, or Zsh):
$ sed '$ s/.$//' <<< $'line one\nline two'
line one
line tw
To update the input file too (do not use if the input file is a symlink):
sed -i '$ s/.$//' somefile
On macOS, you'd have to use -i '' instead of just -i; for an overview of the pitfalls associated with -i, see the bottom half of this answer.
If you need to process very large input files and/or performance / disk usage are a concern and you're using GNU utilities (Linux), see ImHere's helpful answer.
Removes one (-1) character from the end of the same file. Exactly as a >> will append to the same file.
The problem with this approach is that it doesn't retain a trailing newline if it existed.
The solution is:
if [ -n "$(tail -c1 file)" ] # if the file has not a trailing new line.
then
truncate -s-1 file # remove one char as the question request.
else
truncate -s-2 file # remove the last two characters
echo "" >> file # add the trailing new line back
fi
This works because tail takes the last byte (not char).
It takes almost no time even with big files.
Why not sed
The problem with a sed solution like sed '$ s/.$//' file is that it reads the whole file first (taking a long time with large files), then you need a temporary file (of the same size as the original):
Just a remark: sed will temporarily remove the file.
So if you are tailing the file, you'll get a "No such file or directory" warning until you reissue the tail command.
I find the first read-whole-file-into-memory approach can be generally quite useful (less so for this particular problem). You can now do regex's which span multiple lines, for example to combine every 3 lines of a certain format into 1 summary line.
For this problem, truncate would be faster and the sed version is shorter to type. Note that truncate requires a file to operate on, not a stream. Normally I find sed to lack the power of perl and I much prefer the extended-regex / perl-regex syntax. But this problem has a nice sed solution.