public class BackupService
{
    private readonly string _connectionString;
    private readonly string _backupFolderFullPath;
    private readonly string[] _systemDatabaseNames = { "master", "tempdb", "model", "msdb" };

    public BackupService(string connectionString, string backupFolderFullPath)
    {
        _connectionString = connectionString;
        _backupFolderFullPath = backupFolderFullPath;
    }

    public void BackupAllUserDatabases()
    {
        foreach (string databaseName in GetAllUserDatabases())
        {
            BackupDatabase(databaseName);
        }
    }

    public void BackupDatabase(string databaseName)
    {
        string filePath = BuildBackupPathWithFilename(databaseName);

        using (var connection = new SqlConnection(_connectionString))
        {
            var query = String.Format("BACKUP DATABASE [{0}] TO DISK='{1}'", databaseName, filePath);

            using (var command = new SqlCommand(query, connection))
            {
                connection.Open();
                command.ExecuteNonQuery();
            }
        }
    }

    private IEnumerable GetAllUserDatabases()
    {
        var databases = new List();

        DataTable databasesTable;

        using (var connection = new SqlConnection(_connectionString))
        {
            connection.Open();

            databasesTable = connection.GetSchema("Databases");

            connection.Close();
        }

        foreach (DataRow row in databasesTable.Rows)
        {
            string databaseName = row["database_name"].ToString();

            if (_systemDatabaseNames.Contains(databaseName))
                continue;

            databases.Add(databaseName);
        }

        return databases;
    }

    private string BuildBackupPathWithFilename(string databaseName)
    {
        string filename = string.Format("{0}-{1}.bak", databaseName, DateTime.Now.ToString("yyyy-MM-dd"));

        return Path.Combine(_backupFolderFullPath, filename);
    }
}