Solution 1:

The executable is named ctags-exuberant.

The answer could be found using dpkg -L, that shows a list of all files provided by a package. In your case you should see something like the following:

$ dpkg -L exuberant-ctags
/.
/usr
/usr/bin
/usr/bin/ctags-exuberant
/usr/share
/usr/share/doc
/usr/share/doc/exuberant-ctags
/usr/share/doc/exuberant-ctags/FAQ.gz
/usr/share/doc/exuberant-ctags/changelog.Debian.gz
/usr/share/doc/exuberant-ctags/copyright
/usr/share/man
/usr/share/man/man1
/usr/share/man/man1/ctags-exuberant.1.gz

Files in /bin, /sbin, /usr/bin and /usr/sbin are executables (i.e. commands).