Steam has the bad habit to not run after upgrades of the Steam software.
This is, because it uses its own libc which expects libraries not there in Ubuntu.
To fix this, delete the file
libstdc++.so.6.0.18 from the following folders:
Update October 2016
It seems Steam has a few more bad duplicates to make it fail with Ubuntu 16.10.
This command removes all bad libs from the Steam distribution:
find ~/.local/share/Steam/ubuntu12_32/ \( -name "libgcc_s.so*" -o -name "libstdc++.so*" -o -name "libxcb.so*" -o -name "libgpg-error.so*" \) -print -delete