Its possible, how easy it is depends on what information you are after, and whether there are any sites offering it in an easy to grab format, like xml. Try searching on google for xml and whatever kind of information it is you want to grab.
If you need to extract the data from an html page that you know the basic format of, then [man]regular expressions[/man] are probably your best bet.
basically:
1) read the html page into a string using the file(), or fopen and fread() functions.
2) parse the html with regular expressions for the data.
3) write the data to the database.
One thing to be aware of, especially with stock data, there may be legal restrictions on grabbing like this.
Sam