We had ORA-00018 problem in one of our database in data center, in fact, the application users suddenly have been increased and we were not informed about it, so as soon as the default sessions limit went off, the database blocked all new sessions, and even if we were connecting to database with SYS, it was reporting somewhat, database is not available... though there was't any error reporting in alert-logs except few session waiting too long in queue. This could be because of session queue was over loaded and it was keeping all new database connections in queue for too long.
I followed this thread. to resolve it, though the terrible part of the story is, it can only be solved by bouncing the instance... So we had to wait until working hours :(
SPECIAL NOTE: if you are having this problem in RAC environment, then you should give a look to Riyaj Post