This article describes maximum transmission unit (MTU) http://en.wikipedia.org/wiki/Maximum_transmission_unit. It states that IP hosts must be able to process 576 bytes for an IP packet. However, it notes the minumum is 68. RFC 791: "Every internet module must be able to forward a datagram of 68 octets without further fragmentation. This is because an internet header may be up to 60 octets, and the minimum fragment is 8 octets."
Thus, safe packet size of 508 = 576 - 60 (IP header) - 8 (udp header) is reasonable.
As mentioned by user607811, fragmentation by other network layers must be reassembled. https://tools.ietf.org/html/rfc1122#page-56 3.3.2 Reassembly The IP layer MUST implement reassembly of IP datagrams. We designate the largest datagram size that can be reassembled by EMTU_R ("Effective MTU to receive"); this is sometimes called the "reassembly buffer size". EMTU_R MUST be greater than or equal to 576