How can I exclude some files / directories from a tar file?

You can exclude files or directories from a tar file like so:

tar -cvf x.tgz /home/user/  --exclude "/home/user/logs"

where x.tgz is the resulting file, /home/user/ is the directory to backup, and /home/user/logs is the directory to exclude.  

You can also put all the files / directories into a file, and use the -X switch to exclude all files / directories in the file.

NOTE: you need to use the full path to the file / directory to have it properly excluded from the tar.