I'm beginner on arduino, and I'd like know if there are some way to connect to internet without ethernet shield just using an arduino plugged on my computer using a usb cable?
My solution, coming from a software developer by trade, would be to write a small program that would run on the computer and act as the middleman: translating messages sent by the Arduino, fetching URLs and sending results back to the Arduino. Overly complicated I'm sure.
Your Arduino would not be directly connected to the internet. It would be connect to your pc like a I/O card and the pc would be connected to the internet, and to use the Arduino as a I/O card is quite common.
If you feel that a PC is a little bit expensive, you can look into those guys that connects Arduino to a Raspberry PI with just this intention.
You could create a PPP link over the serial port: http://en.wikipedia.org/wiki/Point-to-point_protocol , although I'm not sure how to get Windows to proxy the internet connection to a PPP connection. It's definitely possible in Linux.