To check open and active connections to sqlserver.

FOLLOWING SYNTAX WILL SHOW NO OF CONNECTIONS FOR EACH DATABASE.

SELECT 
    DB_NAME(dbid) as DBName, 
    COUNT(dbid) as NumberOfConnections,
    loginame as LoginName
FROM
    sys.sysprocesses
WHERE 
    dbid > 0
GROUP BY 
    dbid, loginame

 TOTAL CONNECTIONS.

SELECT 
    COUNT(dbid) as TotalConnections
FROM
    sys.sysprocesses
WHERE 
    dbid > 0 

GET MORE BY RUNNIGN FOLLOWING.

sp_who2 'Active'