I feel that the other answers, while undoubtedly useful, do not answer exactly what you asked for... that is, whether Samba is running, but either whether Samba was installed at some time (by looking at files on disk, which might be left over) or whether Samba is installed with the system's knowledge, which might not be always the case.
dpkg will not tell you whether Samba is installed; it will tell you whether it was installed using dpkg/apt or not. If you install Samba from scratch via a tarball, for example, the whole Ubuntu installation system will truthfully tell you that it's not aware of Samba ever having been installed... even if Samba is up and running.
To verify that samba is installed you do indeed try to run it:
If installed (even if it is not running), it will report its version.
The same check can be done with the client part of the Samba suite, which is not necessarily installed with the server:
For the file system support, just in case, you do
mount.cifs -V instead. Strictly speaking this is CIFS support, not Samba.
To know whether the Samba program is running, you can either check the running processes of the Samba suite (smbd, nmbd, winbind):
sudo ps waux | grep "[sn]mbd"
This will return either nothing if the program is not running, or a list of the processes part of the Samba suite:
root 23942 0.0 0.3 299100 15176 ? Ss May24 0:00 /usr/sbin/smbd -D
root 23943 0.0 0.1 298532 4744 ? S May24 0:00 /usr/sbin/smbd -D
root 23944 0.0 0.1 298556 7408 ? S May24 0:00 /usr/sbin/smbd -D
root 23946 0.0 0.2 299092 9504 ? S May24 0:00 /usr/sbin/smbd -D
Or you can verify whether they're listening to ports:
sudo netstat -nap | grep "[sn]mbd"
This will return nothing if the processes are not running, or it will tell you which ports are they listening to:
tcp 0 0 192.168.2.200:445 0.0.0.0:* LISTEN 23942/smbd
tcp 0 0 192.168.2.200:139 0.0.0.0:* LISTEN 23942/smbd
Above, for example, my smbd is listening on ALL (0.0.0.0) remote addresses.
Another way is to check whether anything is listening in Samba's place on TCP ports 139 and 445:
sudo fuser -n tcp 139
This will return either nothing (program not running) or the PID of the running process: