Connections to what? MySQL has a default max_connections of 500..but you, if it's your server, can change that to whatever you like. It is a global setting..it affects all the users on the server.
Max_user_connections is a bit different.
First, to use this feature
you must have 4.0+ MySql. A admin determines this on a per-user basis..it must be setup for each user you want to limit. Normally..this is done to people who have a habit of using too
many resources. Some hosts apply limits to all users across the board...this varies from host to host.
There are other settings that a host may make use of: