Yes Google Docs automatically saves any data you enter into the Google Docs document every 3 to 4 minutes but as soon as you're done entering information into the Google Docs document it's a good idea to go ahead and save the information yourself so that in case a power outage or something else you know that the information was saved.
A doc saves automatically every 3 to 4 minutes but spreadsheets only save when you change a cell and then leave it.
However it won't save on your computer online you have Gears and the Offline feature installed which can be buggy and slow things down.