These are just ten anime that I have seen that anyone who hasn't watched anime should start with. I've seen bits and pieces of many others, but these are just the best of the ones I have seen entirely.
DragonBall Z
Perhaps one of the longest anime ever, with just under 300 episodes and not to mention the 15 or so movies (few of which are official canon). Oh yeah, if you know what filler means, there is a lot of that in this anime; like it could be 200 episodes sans the filler. So yeah, it's not the easiest to just jump into, but it's probably the most famous anime of all time and the most popular, even to this day.
What makes it so great? Well, it's the fighting, plain and simple. The most well-known fight was early on, when Goku had his long, multi-episode and multi-layered fight with Vegeta. And that's pretty much what each saga is about, events that unfold, problems arise, the lesser problems are taken care of, and then all is resolved with a big fight to end the saga.
The show, I believe, still runs to this day on Cartoon Network on Saturdays (the new Toonami that is terrible). But at just one episode a week, it would be way hard for anyone to get into it. When I was a young one, this show was on the daily Toonami block, when they aired both an afternoon and midnight block. I also collected pretty much all the VHS's of the series from the Trunks saga on.
Luckily for all of you, the box sets of each saga are being released at this time. They are up to the Trunks saga, with the Cell Saga upcoming. So you can probably get the whole series for just a fraction of what it cost me to buy the VHS's when they were new, lucky you.
Score: 87/100
Gundam Wing
Also an anime from the good ol' Toonami days. This one is easier to get a hold of, with $30-40 on both halfs of this 49 episode series to find on the internet, or even at a Hastings near you.
This anime is great because it does the mecha thing with a bit more intelligence than most anime. Not only is there an epic war on earth and in space, but there is just a ton of character elements and it all fits together nicely. And just like DBZ, you're here for the battles.
If you really want to put a cherry on this anime, you have to see the movie Endless Waltz, which is just a good movie on its own.
Man, I almost want to break out my toys and set them up, but I'm a man, I'll have to wait until after work.
Score: 91/100
InuYasha
Here's the most well-known of the Adult Swim anime, and the only one that still runs regularly on the block, though only late at night, which would be early morning.
I began liking this show when if first came out, then once I lost track of things I kinda disliked it for a while. Probably as a result of it being the last remaining anime on AS, I have come to like it more and more.
You should watch it for the storyline that is every bit as complicated as DBZ, with just as many twists and turns. Where most anime fail at the side stories that mean little, Inuyasha runs many interesting side stories in most of the episodes. It is because of this that you can jump into this long series at almost any point, which actually doesn't have a conclusion, for whatever reason.
Yes, the manga is still in production, but the anime is stopped. I still say jump in because I imagine they will pick it up at some point. Worst case scenario if you like the anime, you'll read the manga to see the rest of the story.
Score: 82/100
Trigun
Ah yes, the one anime I knew about as a child and had no clue what it was about. Once this anime aired on AS I finally got to see why this series is so well-loved.
I'll be honest, I'm not crazy about Vash and his anime, but that doesn't mean it's worth missing. It could be because this show got a very short run on AS; probably just three or so re-runs.
It's a great anime, and the conclusion is one for the ages, but it's not something I have to own. Not to mention the box sets costs way out the butt and the show no longer runs on AS.
Score: 76/100
Outlaw Star
I only got one look at this while it was on TV, and many years later this anime rattled to the front of my brain and I picked this up on amazon.com for about $30. What a good deal!
This series turned out to be so much better than I remembered and seeing it uncut was very much more mature (one of the late episodes not withstanding). I like the humor, the action is short but sweet, and the side stories are great.
I'm not doing it justice with just three short paragraphs, but know that this is one of the least known, yet one of the best anime out there.
Score: 96/100
Evangelion
Yeah, costs a bit much, but well worth it. It had like a two-run go on AS, and that was it.
This is a dark, sexy, cool anime that combines symbollic elements of anime with the mecha genre. Don't think there isn't some fun and hot shower scenes abound, but there is just the main story and the obvious dark nature. And that's it, it's a simply good anime.
Score: 93/100
Blue Gender
Here is actually an example of an anime that was not as good as I remembered it being. It had a short run on AS as well, and it too is up for half the price of a game.
This anime goes down a darker road than any of the above anime combined, and the whole series is driven by the character of Marlene who is one of the more memorable characters in all of anime - the ending credit sequence probably a big part of that.
The key moments of the anime stayed with me since I saw this one so long ago, but those moments, while still great, did not represent the parts in between. Basically, this is a good anime, but it is a bit corny at times. It's not the smartest anime ever, but still worth watching.
Score: 85/100
Afro Samurai
Okay, so what makes this 5-episode anime so great is that it does everything right. It's a quick story that gives you everything an anime can offer, including but not limited to over-the-top violence, sex, and a unique art style. Not to mention there is a hip-hop layer of coolness poured on top of it all that does not get in the way; it, in fact, works. The fights to get to the main villain are some of the best fights in all of anime.
Score: 90/100
Elfen Lied
The image provided speaks to nothing about the anime, it's just the coolest and probably the only "clean" one out there to show (looks cool too). This image may actuallylead you to believe this is some heartsy, lovie-dovie anime. This image does nothing but show the main character; well, at least half of her and with probably 100% more clothing than you usually see on her (yeah).
No, this is not a hentai either. This anime does gratuitous violence and gratuitous boob-shots like no other. But that does not mean this is a shallow, cheaply done series with no substance. All of that is there to further enhance the emotions of seeing what horrors these characters go through.
Trust me, this is ADULTS ONLY, and even if you are an adult, please only watch if you have a tough stomach and can bare witness to some of the tougher-to-watch scenes. It's not a "hard to watch" anime, it's just not for the light-hearted. This is by no means a happy anime, and maybe it's not the easiest to swallow conclusion, but it's worth watching if you dare.
It should also be noted that the manga is very different, though, no English translation as of yet.
Score: 97/100
Cowboy Bebop
Yes, here you are, the best anime I have seen. This was the first serious anime to run on Adult Swim, and though it looked odd from the outside, once I saw it I could not stop watching. Keep in mind, this was when I was still pretty young.
The reason this anime is so great is because it does everything in a fashion that is very un-anime. This is probably the only anime where every episode could completely stand on its own for viewing; the two paired episodes could even maybe stand alone.
This series does everything right: humor that makes you laugh, action that can be watched over and over, side stories that almost trump the main story, top quality animation even though the series is about a decade old, and when every character is so well fleshed-out that you don't know if you like the main character better than the dog, you know the characters are well built.
There are just like two episodes that I could do without, but I would stop to watch all of them if they were still on TV. Now that I finally have the whole series thanks to amazon.com I can watch it any time I want.
(Here's a true and completely off-topic tid-bit: my favorite episode "Ballad of Fallen Angels" reminds me of the night when I was as sick as anyone can get. It was like my body let me watch the episode, but as soon as it was over that was when I went on a like 36 hour vacation in the bathroom. Trust me, it's exactly as bad as you think. Like, my God, where was it all coming from?)
Score: 99/100
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Honorable Mentions: Paranoia Agent, Fooly Cooly, Case Closed, Lupin the Third, Death Note (even though I haven't seen it all), Samurai Champloo, the original batch of Pokemon episodes, and Big O. All were on Adult Swim at some point, exept for Pokemon. You may laugh at me taking the Pokemon episodes serious, but the first "saga" and the first movie were actually pretty good.
It doesn't matter what you like, there is an anime for you. Though for me, I look for action and/or strong stories.