There is no practical limit that I know of. If there is a limit, it is extremely high. However, each connection requires a certain amount of DB2 instance memory, usually about 64K, but the exact amount of memory can vary depending on a number of factors.
With DB2 ESE (Enterprise Server Edition), one can activate the connection concentrator that allows multiple inbound connections to share one connection on the DB2 Server. If you don't have DB2 ESE, then connection pooling software can be used on the application server such a DB2 Connect, Websphere AS, Jboss, WebLogic, etc. Even for those using DB2 ESE, most shops do not enable the connection concentrator on the DB2 server and instead use connection pooling on the application server.