I don't watch much anime but loved sword art online, I have

Sword Art online was shit and I dropped it seven or so episodes in. Whatever episode was about a poop sword that had the blacksmith girl falling over the main character.
Try Kyousou Giga, Fafner, Eva, Dennou Coil, Kino no Tabi, and Mononoke.
Also note when I say Mononoke, I mean Mononoke, not princess Mononoke.

>>164218
SAO is a popular "entry level" anime. There are a lot of people who love it, which is fair, but a lot of people who have watched a lot of anime really despise it, for good reason.

But this isn't the thread for that. What you want is Tengen Toppa Gurren Lagann.

>>164253
Also: Death Note.
https://www.youtube.com/watch?v=x-xpMRCnJRE

>>164218
SAO is shit. Watch Psycho-Pass

>What should I dive into now if I want exciting and thought provoking plots and storylines?
If your frame of reference for this is SAO you have set the bar awfully low. I don't consider SAO to have either of the qualities you listed there so I'm nonplussed about how to proceed. I'd say the usual entry level recs would be a safe bet though, stuff like Cowboy Bebop, DBZ, FMA, Trigun, Big O etc. Shows like that are very accessible to people who don't watch anime and have broad appeal. I could recommend you stuff with a similar premise to SAO: Overlord, No Game No Life, Log Horizon, and I guess KonoSuba, but since your conditions were about "thought provoking storylines" and such not sure if they'd be what you want. If I were going for "thought provoking" I'd say Serial Experiments Lain, Legend of the Galactic Heroes, Tatami Galaxy, and Ghost in the Shell: Stand Alone Complex (which is actually often listed as an entry level title).

>Also is Sword Art Online considered good according to you people?
If by "you people" you mean the kind of people who answer anime recs on /wsr/, which are often bored /a/nons, then no. /a/ hates SAO, as do most communities with a sizable population of veteran anime watchers. That's ultimately just the general opinion of this community though. There are other communities out there who like it. SAO is actually a very popular show in general, both in Japan and the west, but mainly with casuals who don't watch a whole of anime. There's very little consensus about "good" anime because critics are not paid much attention in the anime scene, it's more about just picking whichever community you like best and following their taste for guidance, but some of those entry level titles I listed are among those with near-universal acclaim.

>>164218
If you want exciting and thought provoking storyline you won't get recommendations similar to SAO. I'm going to list some shows that I think fit the criteria above, but take note that that's my entirely personal taste. Whether or not you'll like it is something you can only find out by watching.
>Neon Genesis Evangelion
One of the classics and highly acclaimed by most anime fans. At first you'll probably think it's a show about giant robots fighting giant aliens. It actually is a psychological drama, with most of the focus being on the characters, their inner worlds, pasts and interactions. It also explores some basic philosophical questions about what it is to be human, why being close to others is such a difficult thing to do etc. It's not an easy watch but worth it. The protagonist is a crybaby which might be off-putting for you. Watch the original anime, then the End of Evangelion film.
>Re:Zero
Like SAO, it's a show with the premise of a young man being trapped in another world. It's a deconstruction of that genre to some degree, as the MC doesn't magically do everything right and suffers a lot due to his own flaws. In essence it's poking fun at the genre, and I suggest you watch it after you get sick and tired of the premise which should happen once you've seen a bunch of shows applying it.
>The Grave of the Fireflies
Story about a young boy and his little sister in Japan during the end days of World War 2. Not easy to stomach but very moving. It's a movie, so you can watch it in one go.

Otherwise, the suggestions others have made in this thread are pretty solid. Except for Gurren Lagann. It's good but doesn't fit your criteria. If you need silly, over the top action and craziness I suggest you give it a shot though. Oh, and the more mature genre of anime in general is called Seinen.