tl;dr: Person of Interest is the best science fiction TV series of recent years. You should watch it.
At this point, I hear some of you saying, "Wait -- Person of Interest? Science fiction? Isn't that a police procedural or something like that?" Books, covers, and like that -- bear with me.
The best definition I know of "science fiction" is that it is about *ideas*. Great SF takes an idea or two, asks "What if?", and runs from there, exploring the implications of that idea. It's not about spaceships and aliens -- it's about those ideas.
The core idea of PoI is that there is a Machine, a sophisticated and increasingly sentient AI that is plugged into the Internet. It sees all, knows all, and is getting ever-better at *predicting* all. You need to accept that central conceit for the series to work. It's worth suspending disbelief there: while I personally don't think it's plausible *yet* (and there are some chaos-theory reasons to believe it'll never happen to quite this degree), the story pays it off well with a fine exploration of where things could eventually go.
Our primary protagonist is Harold Finch, inventor of the Machine. He built it for the government, and the Machine is feeding the government "relevant" information -- predictions of terrorist attacks, assassinations, and other such matters of Strategic Importance.
The problem is, the Machine sees all, including the far larger number of "irrelevant" matters -- the little deaths and tragedies of ordinary life. So it begins to feed Harold hints of those tragedies, in the form of numbers that identify the relevant people. Harold is a programmer, and an injured one at that, unable to address these problems himself, so he hires Mr. Reese -- ex-military, ex-CIA, cool to the point of scary -- to look into these cases and try to save lives.
That's where the series starts, and season one *is* a something of a procedural. (I gather. I didn't come in until somewhere in the middle of season two. I recommend starting from the beginning; figuring out the moving parts in the middle isn't simple.) As the story progresses, it picks up some of the expected sorts of arc -- the government wanting more control over the Machine, Mr. Reese's past catching up with him, etc -- but it's all fairly ordinary for the first couple of seasons.
And then the network apparently stopped interfering so much, and allowed Jonathan Nolan to tell the story he *wanted* to tell. In season three, the story begins to really explore the ramifications of the scenario: the dangers of ubiquitous surveillance, and the tragedies that can happen when the eyes in the sky get it wrong. Suffice it to say, this series is a bit like Dollhouse: if you're turned off because the scenario makes you queasy, trust me, the show-runner is *way* ahead of you, and the story is *much* darker than it looks at first glance.
That begins to set up in season three; seasons four and five play it out, as we explore just how terrifying the world could be with an omniscient AI trying to save humanity from itself, especially if you get on its bad side. This is a story about a Singularity happening so quietly that almost nobody knows it's even occurring, and the small group who are trying to stop it. I found the final half-season to be utterly gripping, and the writers took the opportunity to bring it to a solid close. (They have left the door open for a possible sequel, but that will clearly be a different story, in different circumstances with different characters.) In terms of flavor, the best comparison I can make to the later seasons is the SF novel Iron Sunrise. No, I won't say why.
The cast is excellent, and it gradually extends beyond those two characters. The first couple of seasons include a pre-Empire Taraji P. Henson, and Amy Acker gets to play the role she was born for, as Root, self-proclaimed high priestess of the Machine -- a badass sociopath who gradually learns how to be human over the course of the story. The writing is solidly good, and they do a good job of varying the tone even in the grimmer later seasons. (My favorite episode is in season four -- told mainly from the viewpoint of the Machine itself, it is weirdly funny and deeply sympathetic, driving home just how differently it sees the world.)
Overall, it's well worth watching. The individual episodes stand by themselves reasonably well, but by the second half this is a strongly arc-driven story, taking its premise and exploring it richly. I find myself much more eager than I might have expected for HBO's upcoming Westworld series -- also by Jonathan Nolan, and also promising deep explorations of AI and its interactions with mankind...