If you use MIDP 1.0 with no extension packages that is not directly possible. However, it is somehow possible as follows. Two MIDP applications make http requests to a same server and they exchange their data on the server.
More direct connection is possible via SMS. Nokia SMS API and Wireless Messaging API enables sending and reciving of SMSs in a MIDlet. Nokia SMS API is supported in Nokia 3410. At least Nokia 3650 will support Wireless Messaging API.
In the future, MIDP 2.0 will include socket support. In addition, bluetooth APIs will make short distance connectivity easier.