Experienced email users know that you should never respond to spam. Don't click links in the message just to see what they're about. Don't send back a tirade blasting the spammers and telling them to stop bothering you. Don't even click the "unsubscribe" link. Spammers spew millions of messages to address lists that contain both valid and invalid addresses. Any response at all lets them know your address is "live," making it more valuable when they sell it to other spammers. But that's not the only reason to delete dubious messages without responding.
Every email message comes with a header that identifies the message's sender, subject, date-time stamp, and so on. Beyond these visible message attributes the header also reveals the route that the message took, server by server. By following that list back to the beginning a recipient can identify the server from which your mail originates.
Letting them know your mail server address doesn't sound like a big problem. However, by using geolocation the recipient can get a rough idea of that server's location. Many websites provide this service; just search for "Geolocation". Geolocation isn't always accurate, and can be fooled if you’re using a VPN for example, but more often than not geolocation correctly identifies your region.
Now the recipient can use a tool like ZabaSearch (in the US) to get your home address and phone number by searching on your name and region. The more uncommon your name, the more likely this type of search will work. Other services like Spokeo (or PeekYou in the UK) will reveal even more information about you.
Granted, not all of the online information is accurate. Spokeo in particular has been sued over inaccurate information, but much of the online data is correct, and a sleuth willing to go beyond the free services can find out even more.
So there you have it. At the start, Sam Spammer has nothing but your email address, and no guarantee that it's valid. If you respond, Sam can parlay that guess to learn much more about you. He can get your home address, phone number, age, marital status, perhaps the value of your home, and more. The sender doesn't have to be a spammer, of course. It could be any stranger emailing you for the first time. To protect your identity, don't respond to spam or other dubious email – ever.
For more on this topic, see our tips on beating back the tide of spam emails.