Is it posible to connect atmega 328 to a serial port?

Hi,

As already stated, you can't connect it directly, but if you're looking for a few options of how to do it with some intermediaries that will save your ATmega this page has a decent explanation and a few handy links. Also the MAX232 chip referenced in that article for $1-3 I see routinely for far cheaper (link to an example).

Cheers ! Geoff