Few things others might have already said.

-Great relationship with third parties.
-They don't try to reinvent the wheel. If it's not broke, they don't try to fix it.
-consistency
-If they see something that works, they "borrow" it. If you get a Sony console, you're not missing much.

Sometimes a PlayStation console is the most powerful. Sometimes, it's the least. It's always going to be good enough to define the generation.

Sony don't half-ass efforted on the consoles, a good library with strong support from third parties and freedom to first party to show their creativity. Also consistency, Sony have kept consistent with their consoles and support never abandoning a system to early.

For the same reason fifa and cod sell each year

Which is...?

Easy question, i think. The BEST and the MOST Games in the Gaming-History, thats the reason :)

Perfect West & Japan-Support. And the PS2 & PlayStation 4 are the best Console's of all time!

They basically stole the Super Nintendo set-up which Nintendo had created and then paid off third parties to cut Sega out of the industry via money-hats.

They've stuck to that formula and don't make a lot of mistakes which then doesn't give competitors much of an opening. On the home console side, they've made basically one major mistake in 25 years in the business (Blu-Ray for PS3) and still were able to push out a more than respectable 85 million units.

The Playstation is basically the successor brand to the Super NES. They took that setup and locked competitors out of getting it back by using money-hats.

The N64 would have sold 100+ million units if Nintendo had not been stubborn and used CDs, even as a second format (there's no law that says you can't have cartridges and CDs on one system, the Saturn had both). The fact that it sold 33 million with meager developer support and long stretches of 1-2 game releases for $60-$70+ games only for months on end was insane. 

Having Blu Ray on PS3 pretty much made sure HD DVD was pushed out.  It was the cheapest Blu Ray player when the PS3 launched.  I believe most standalone Blu Ray players at the time were still 800-1000 dollars. 

I almost feel bad for the early adopters of first generation Blu Ray players because after awhile they updated Blu Ray to a new version and some of the original standalone players didn't even have a Ethernet or wifi capabilities which turned them into bricks.  PS3 of course could update and was able to play the newer discs.  Basically if you wanted to be early adopter to Blu Ray then it only made sense to buy a PS3 at the time till the standalone players became cheaper.

The standard by most popular yes. I would say Nintendo is still the standard name when you say video games to anyone over mid 30's. More people are going to recognize Mario over Nathan Drake, Ratchet, Kratos, etc.

Over 30s probably Nintendo under 30s probably PlayStation.  I remember my mom calling everything Nintendo back in day even if she was trying to refer to Sega or Sony consoles.

Yeah probably still into the mid/late-90s, "Nintendo" was used as a generic term for every video game by a lot of parents. Playstation did eventually break that.