Doug,
That depends on OS/system.
NXOS supports setting logging level per server:
http://www.cisco.com/c/en/us/td/docs/switches/datacenter/nexus7000/sw/system-management/command/reference/n7k_sm_cmd_ref/sm_cmd_l.html#pgfId-1015086
on IOS you have filtered settings:
http://www.cisco.com/c/en/us/td/docs/ios/netmgmt/command/reference/nm_book/nm_09.html#wp1082864
Additionally your syslog server should be quite adapt at filtering out messages up to certain severity.
M.