Logger module with JavaScript
Interesting question,

You have a ton of repeating code, so don't hesitate to write more helper functions so that this:

genericLogger = new (winston.Logger)({
    transports: [
      new (winston.transports.Console)(),
      new (winston.transports.File)({ filename: './log/error.log' })
    ]
});

dbLogger = new (winston.Logger)({
    transports: [
      new (winston.transports.Console)(),
      new (winston.transports.File)({ filename: './log/db.log' })
    ]
});

viewLogger = new (winston.Logger)({
    transports: [
      new (winston.transports.Console)(),
      new (winston.transports.File)({ filename: './log/view.log' })
    ]
});

networkLogger = new (winston.Logger)({
    transports: [
      new (winston.transports.Console)(),
      new (winston.transports.File)({ filename: './log/network.log' })
    ]
});


could be:

function createLogger( filename ){
  return new (winston.Logger)({
    transports: [
      new (winston.transports.Console)(),
      new (winston.transports.File)({ filename: filename })
    ]
  });
}
genericLogger  = createLogger( './log/error.log' );
dbLogger       = createLogger( './log/db.log' );
viewLogger     = createLogger( './log/view.log' );
networkLogger  = createLogger( './log/network.log' );


I did not test this code, but you get the gist.

Furthermore, in this code, I have no idea what t and n are:

Logger.db = function(t, n) {
    if(n) {
        dbLogger.log(t, n);
    } else {
        dbLogger.info(t);
    }
};

Logger.view = function(t, n) {
    if(n) {
        viewLogger.log(t, n);
    } else {
        viewLogger.info(t);
    }
};


Here as well, you could use a helper function:

Logger.loggerHelper = function( o , t , n ){
  if(n){
    o.log(t,n)  
  } else {
    o.log(t)
  }
}

Logger.db = function(t, n) {
  loggerHelper( dbLogger , t , n );
};

Logger.view = function(t, n) {
  loggerHelper( viewLogger , t , n );
};


After a while I would get irritated by the above as well, and write something like this:

var winston = require('winston');

var Logger = {};
var loggers = {
  generic : './log/error.log',
  db : './log/db.log',
  view : './log/view.log',
  network : './log/network.log'
};

for( logger in loggers){

  Logger['_' + logger] =  new (winston.Logger)({
    transports: [
      new (winston.transports.Console)(),
      new (winston.transports.File)({ filename: loggers[logger] })
    ]
  });

  Logger[logger] = function(t,n ){
    if(n) {
        Logger['_' + logger].log(t, n);
    } else {
        Logger['_' + logger].info(t);
    }  
  }

}

Logger.error = function(n) {
  Logger['_generic'].log('error', n);
};

Logger.info = function(n) {
  Logger['_generic'].log('info', n);
};

module.exports = Logger;


loggers contains the link between the method and the file name, so it becomes now very easy to add/remove/change loggers. This approach does expose a lot more (all) the functionality in Logger, but I think that would work out.