What I fairly meant, it is what the person grew up with that will throw their responses.
I grew up hearing of many, such as Elfen Lied, .Hack//, FMA, Gundam, Cowboy Bebop, Code Geass, Melancholy of Haruhi Suzumiya and probably plenty others I forgotten. (These are mostly Japanese oriented ones)
Does not mean I seen some of those, but those are what I grew up always hearing about. Though as you see, there isn't one I can say is "most" popular. I feel they are all equal as normally one person liked another just as equal.
Pokemon is probably the most well-known amongst people currently in their twenties, though that's also the group that got the highest amount of DBZ exposure; Gundam Wing was there, too. Folks younger than that will be more familiar with Naruto and Bleach.
Cowboy Bebop is probably more popular amongst anime fans, but considerably less well known outside of that group, though its showings on Cartoon Network definitely help it.
One Piece is another anime that has a large recognition amongst anime fans but very little outside of that.
FLCL has achieved legendary status amongst anime fans, but once again there's little mainstream recognition.
If you dig a little deeper, you'll find that Madoka has still heavily impacted all of anime fandom. It gets bonus points for its recency relative to all these other titles.
After that, you'll come across most of the "required reading" titles like Azumanga Diaoh!, Evangelion, Trigun, etc.
This is difficult question because it spans a number of different generations.
For some it might be Sailor Moon, Yu Yu Hakusho, Rurouni Kenshin, Akira, Ghost in the shell, Inuyasha, Dragon Ball Z, etc.
Among people who are more into anime you'll have answers like Neon Genesis Evangelion, Serial Experiments Lain, Cowboy Bebop, Samurai Champloo.
In younger people it'd more likely be Naruto, Bleach, One Piece, etc.
Depends. I'd say all things considered as one, Pokemon is the only real universal answer. The most interesting part of this question lies in archetypes, and how older works set precedents, or cumulatively influenced newer ones. I'd say people know more about older anime than they realize. And even those works of art are extensions of older methods of storytelling and art.
Overall: DBZ is the probably the number one most well known anime. Not in the terms "a matter of opinion". It probably, literally is, the topmost of the tops. It came out a time where older generations, and my generation (which was at that time still very young) were exposed to it. My dad used to watch it on a daily with me, and he doesn't even know what the word anime means.
Most of the present "mainstream" tops like Naruto, Bleach, and One Piece, have all admitted to admiring and drawing influence from DBZ in one degree or another. And for the most part, DBZ just helped amplify some of the big stereotypes in that usually make their way in most anime and manga. But I digress. If you're looking for well known and generally popular you would have DBZ along with some other series that have gained considerable popularity over the years. Anything with children and monsters seemed to have been big; Pokemon, Yu-gi-oh, the Digimon series....
A good way that used to exist to measure what animes were the most popular in an overall audience (including non-anime fans) would have been to watch, back in the day, Toonami on Cartoon Network. If you can't understand why or how: why would station that depends on an audience attuned to animated series choose to dub the worst? Toonami took the cream of the crop; big, popular, animes from Japan would inevitably find there way here. In some cases, they still somehow find their way here.
I know Toonami exists today after popular demand brought it back, but I don't really care to watch it, nor am the hugest anime fan as I was once; so your best bet is checking a manga website. Most of those free websites people use will have the most frequently viewed manga; the last time I read manga, Naruto, One Piece and Bleach were still at the top in that order, though if I remember correctly, on another website Naruto and One Piece switched places. Now-a-days; I don't know.