This seems very high. Do you have a lot running on the server? You should really get an admin to have a look at the server as I think there are some processes that may be using up lots and lots of memory.
Use top and order by memory usage to see the offending entries.
This systems is a dedicated MySQL server running RHEL 5 in 64bit mode. Nothing else is running on the system. I have a lot of connections (max_connections) set to 2048 and I've hit that max number many times.
I think I might be at the point where I need to look in to getting a MySQL consultant to help tune the database.
How is you application connecting to the database? Are you using persistent connections or non-persistent? Are you opening up a connection and never closing it which means that it keeps the process alive and could explain why you are running out of connections.