WordPress can’t connect to DB: Too Many Connections, in a very small site

I’m building a website in WordPress, and during this week it started crashing with the Error establishing a database connection message. I created a test archive that only connects to the DB and it tells me the error is “too many connections”

I’m pretty sure that I’m the only one that visits the site (I’m still developing it, and the apache logs don’t show more visits), the WordPress Backup to Dropbox plugin is the only one I think could be using the database a lot, but still I don’t think I should see that error.

The output of “show processlist” only shows me the “show processlist” query.

And the output of “show status like ‘%con’” is this:

+----------------------------------------+--------+
| Variable_name                          | Value  |
+----------------------------------------+--------+
| Aborted_connects                       | 41002  |
| Com_show_contributors                  | 0      |
| Connections                            | 337541 |
| Max_used_connections                   | 152    |
| Performance_schema_cond_classes_lost   | 0      |
| Performance_schema_cond_instances_lost | 0      |
| Ssl_client_connects                    | 0      |
| Ssl_connect_renegotiates               | 0      |
| Ssl_finished_connects                  | 0      |
| Threads_connected                      | 151    |
+----------------------------------------+--------+

threads connected seems to be always at maximum

What can I do? Is this a server issue?

Edit: As @Giacomo1968 answer suggests I ran a the MySQL Tuning Primer Script, but it died with the too many connections error, the output was as follows:

        -- MYSQL PERFORMANCE TUNING PRIMER --
             - By: Matthew Montgomery -

MySQL Version 5.5.36-cll x86_64

Uptime = 0 days 0 hrs 56 min 33 sec
Avg. qps = 59
Total Questions = 200437
Threads Connected = 151

Warning: Server has not been running for at least 48hrs.
It may not be safe to use these recommendations

To find out more information on how each of these
runtime variables effects performance visit:                                                                                                                                                    
http://dev.mysql.com/doc/refman/5.5/en/server-system-variables.html
Visit http://www.mysql.com/products/enterprise/advisors.html
for info about MySQL's Enterprise Monitoring and Advisory Service

SLOW QUERIES
The slow query log is NOT enabled.
Current long_query_time = 10.000000 sec.
You have 4127 out of 200644 that take longer than 10.000000 sec. to complete
Your long_query_time seems to be fine

BINARY UPDATE LOG
The binary update log is NOT enabled.
You will not be able to do point in time recovery
See http://dev.mysql.com/doc/refman/5.5/en/point-in-time-recovery.html

WORKER THREADS
Current thread_cache_size = 0
Current threads_cached = 0
Current threads_per_sec = 4
Historic threads_per_sec = 2
Threads created per/sec are overrunning threads cached
You should raise thread_cache_size                                                                                                                                                              

MAX CONNECTIONS
Current max_connections = 151
Current threads_connected = 150
Historic max_used_connections = 152
The number of used connections is 100% of the configured maximum.
You should raise max_connections

INNODB STATUS
Current InnoDB index space = 448 K
Current InnoDB data space = 3 M
Current InnoDB buffer pool free = 82 %
Current innodb_buffer_pool_size = 128 M
Depending on how much space your innodb indexes take up it may be safe
to increase this value to up to 2 / 3 of total system memory

ERROR 1040 (08004): Too many connections