1. Dial-up internet. Considering how far the internet and the ways of connecting to it have evolved in the past 10 years, I think it's safe to say that dial-up service won't even be offered in 10 years, and almost everybody will be hooked up wirelessly. In fact, it's kind of obsolete now, but a small minority still uses it.
2. Home phones. The vast majority of people in this country (over the age of, say, 15) own cell phones, and many people don't even use traditional house phones any more. I almost never use mine, unless I misplaced my cell phone (and then it's very handy for locating it). Kids are getting cell phones at younger ages every year, so at some point, home phone service will die out.
3. CDs. With the rise of MP3s and music downloading, CDs are on the way out. People still use them now, but 10 years from now, they'll be like the cassette tapes of yesteryear.
Of course, I was thinking purely in terms of technology, since that seems to develop at a ridiculous pace, and new gadgets come and go all the time, getting more advanced every year. 10 years ago, I was using my dad's computer with a big, clunky monitor, and I think we had DSL internet, which was pretty good back then. I didn't have a cell phone (and didn't want or need one), and CDs and DVDs had pretty much replaced cassette tapes. 5 years ago, I was using my own computer and replaced the big, clunky monitor with a new, sexy flat-panel. I was usually hooked up to the college internet, but we had just gotten wireless at home. I got my first cell phone almost 5 years ago, after I graduated and my parents harrassed me into it. I still used CDs, but I also listened to MP3s on my computer. Now, I use a small laptop with a touch screen and have Fi-Os. I'm on my 2nd cell phone, and I recently bought an iPod Touch and transferred most of my music onto it (I can also browse the web, read Kindle books, play games, etc.). So I'm interested in seeing what technology will be like in 10 years. Maybe I'll have a robot maid, that would be awesome.