Even in this era of wireless mobile phones, the good old landline may still have one interesting advantage over them: Using a landline to call 911 means the emergency operator will instantly know exactly where you are located, and will dispatch emergency services immediately. By contrast, mobile phones may or may not provide an exact location to the emergency operator. In some cases, police/fire/paramedics may waste precious minutes driving around the neighborhood trying to find you. In other cases, the mobile phone may provide an exact location. Would you want to risk the possibility of your location being obscured in an emergency?
In the USA, telephone companies must provide access to 911 service on all landlines, even if you are not currently paying for service on them. For this reason (and others), I recommend that everyone who has access to a landline phone jack should keep an old phone plugged into it just for quick access to 911. (Eventually this requirement may change and free 911 access may go away; but as far as I know, this is not going to happen any time soon. The old landline system is extremely mature and very slow to change.)
For best results, the type of telephone you use should be as simple as possible: It should have a touch-tone keypad (not a rotary dial as that is much slower to use) and a handset, and should not require power from the wall. That is, it should be the type of phone that only runs off the power provided by the phone jack itself. This means that you can call 911 from the landline even if your main electricity goes out, because the phone company is required to provide their own back-up power to landlines. (Unless of course the utility poles are knocked down in a storm, in which case the landlines may be knocked out along with the electricity). You can often find such telephones at thrift stores for under $10.00. I found mine at Goodwill for about $7. Cordless phones or memory phones should not be used, because they require wall power and will become useless during a power outage.
In America, our landlines are still incredibly reliable and robust. Service outages and downtime is very rare. Unlike with mobile phones, there is never an issue with poor reception or dying batteries. Therefore, it is good practice to keep a telephone plugged into the line at all times for quick, easy access to 911.