アプリケーション側でエラーとなり、MySQLへのコネクションをが残っていて
どんどんconnectionが残り続け、結果connectionが溢れてしまう事がある。

デフォルトでは、MySQL側でconnectionを8時間保持し続けます。

mysql> show global variables like 'wait_timeout';
+---------------+-------+
| Variable_name | Value |
+---------------+-------+
| wait_timeout  | 28800 |
+---------------+-------+
1 row in set (0.00 sec)

wait_timeout = 360

wait_timeout を減らすと、その分スレッドをthreadを生成してThreads_createdが増えていくし、
connectしたりするオーバーヘッドも大きくなります。
そこでthread_cache_sizeを増やしてやると、オーバヘッドがなくなります。
thread_cache_sizeは、max_connectionsと同じくらいで良いと思う？？

mysql> show global variables like 'thread_cache_size';
+-------------------+-------+
| Variable_name     | Value |
+-------------------+-------+
| thread_cache_size | 0     | 
+-------------------+-------+
1 row in set (0.02 sec)

mysql>  show global status like 'Thread_%' ;
+-------------------+---------+
| Variable_name     | Value   |
+-------------------+---------+
| Threads_cached    | 0       |
| Threads_connected | 79      |
| Threads_created   | 6398514 |
| Threads_running   | 21      |
+-------------------+---------+
4 rows in set (0.01 sec)

mysql> show global variables like 'max_connect%';
+--------------------+-------+
| Variable_name      | Value |
+--------------------+-------+
| max_connect_errors | 10    | 
| max_connections    | 100   | 
+--------------------+-------+
2 rows in set (0.00 sec)

thread_cache_size = 100  

wait_timeoutとthread_cache_sizeは、MySQLを再起動せずに反映させる事ができます。

mysql>SET GLOBAL wait_timeout = 360;
mysql>SET GLOBAL thread_cache_size = 100;

http://anothermysqldba.blogspot.jp/2013/09/mysql-optimization-tip-threadcachesize.html

       show status like 'Threads_created';
           set @Threads_created=< result from query above>;
      show status like 'Connections';
           set @Connections=< result from query above>; 
      select 100 - (( @Threads_created / @Connections ) * 100) as "Threads_created % of Connections"\G

So if your execute the process above what is your percentage ? You want this to be as close to 100 as possible. So for example the server I recently encountered had a % under 10%. So how do you fix this and raise your %?