An internet connected hat would really help to google for a really good pickup line when you meet a girl --(eg "Hey Baby, can I buy you a drink or do you just want the money?"). You could also use it to keep track of the baseball score in places like a church or at a funeral.
An internet-connected hat means that you wouldn't need to bother carrying an iPod. You would just upload your playlist and take it from online. The hat would have a solar panel to recharge the battery, so you wouldn't have to worry about recharging, because it would always be recharging.
The best thing about an internet connect hat is that it appears to make you look smart, and you can let it go to your head.