Well, depends which message you refer to. I got an iPod touch te other day, and I discovered you can check your email. And to text, a good quality and free application is called text plus, which you can find in the app store.
Without the use of any apps, no, you cannot send or receive picture messages on the iPod Touch. If you have an iPod Touch, there are two apps that let you SEND picture message, but you cannot RECEIVE...