I'm looking into this for my Mom (she just turned 80). She's been doing great on her own but I'm starting to worry about the "I've fallen and I can't get up" scenario.
I've been through the same situation and checked out the options, but my Mom went to an assisted living center before we got something installed. There are several ways to go, depending on the situation.
You can install a medical alert that will call a monitoring service in the event she presses the emergency button she wears on her wrist or around her neck. These systems do require that she remembers to wear the alarm button and press it in the event of an emergency. For some seniors this isn't a problem, but for others remembering new things can be a challenge. These systems typically cost a couple hundred to have installed and $25 or so per month for monitoring. Google "medical alarm" and you'll see tons of options. Of course, these are the most commonly available because of the monthly service fee that's attractive to businesses.
A similar alternative is to install an unmonitored system (i.e., not monitored by a business). Here's an example. They're no more difficult to install than a phone. Instead of calling a monitoring service, these systems call a list of potential helpers such as yourself, other family members, neighbors, etc. As a result, there is no monitoring fee. If there are potential helpers who keep a cell phone with them all the time and can provide help or can call emergency personnel these are a lower cost alternative. If you go this route, you should make a point of having her test it every week or so just to make sure all is well. Not sure if the monitored providers provide regular testing, but it's worth asking about if you go monitored.
Another alternative, and perhaps a backup, is to install a couple of webcams in areas where she spends a lot of time so you can see that she's up and around. While not necessarily providing immediate attention, it does provide a backup in the event she wasn't wearing her alarm button or wasn't able to press the button for some reason. Of course, giving her a call regularly can accomplish much the same thing.