The ultimate network scanner nmap knows how to perform an UDP scan:
$ nmap -sU -p1-65535 <target>You can add useful options such as -sV (probe open ports to determine service/version info). The scan is much longer than a TCP scan, but sometimes it works. Yes, sometimes. Recently I started a simple UDP server (with socat) on a random port and challenged myself to find it within the whole 1-65535 range: I appeared to be unable to find it with nmap (I'm probably misusing nmap).