Should I get rid of my landline?

The only reason to keep a landline at this point, is if you live in a place where you can't get broadband through some means other than a phone line, like "old" DSL, or you don't own a mobile phone.

There are ISPs who provide alternates to phone-based DSL, and there's the promise of fiber on the horizon.

If you already get your broadband via cable, or satellite, or via a regional ISP over some service that doesn't require an active POTS line, I say ditch it.

I did without a landline for a few years. It was really OK! I only had a concern if the power were to go out. The thing is, it never really affected my cell service. You'll just want to be sure you get great reception at your home, or you'll curse the day you ditched your POTS line.
Now that I'm married again, we have a land line and answering machine, but that's only because we don't want to get each kid a cell phone.

You want to keep at least one landline in case of emergency. If the power goes out at your house, chances are it could also go out at a cell tower. They have backup systems at cell towers, but they also are known to go down, too. Natural disasters, local emergencies, personal trauma; your life shouldn't hang on how many bars you have. The POTS lines have over a century of rock solid use. That's the kind of insurance you want when you expect to hear somebody pick up on the other end. As much as I love my mobile, and as much as I can't stand an oligopoly, I'd still keep the landline.

That said, you can drop your line down to the absolute minimum service if you need to save money. You just need the line. 911 works regardless of what long distance service you may have on the line.