Basically, you don’t want to. One less fan is one less person to argue with.
If you tell someone to watch a show because it’s good, you are putting the show down. Don’t give some sappy monologue about emotions and “it’s more than a cartoon.” That stuff will just annoy people. Also, definitely don’t watch it with them. It generally detracts from the experience unless you are both new to it.
First, they have to be into anime. Don’t use Clannad or something as a gateway anime unless the person discovers it and watches it of their own free will.
Personally, I have a list of gateway anime that I can recommend without making my friend part of a circlejerk I hate. It derives from this video of amazing ED execution, which has spoilers for every anime I’m about to list.
Most of these anime are either considered the best of their season, or widely regarded as forgotten gems.
Steins;Gate - For Scifi fans, reddit-ers, or people active in the bbs age of past. Good introduction to a lot of anime terms and Japanese names.
Code Geass - For fans of strategy games or big robots. It’s a good smart-action anime with enough twists and characters to keep someone interested. It gives viewers a bit of passion for Japan too.
Clannad - For the drama comedy fans. The people close with family get this one, but as I said before, it’s best to let them watch it when they want.
Tokyo Magnitude 8.0 - Good for the documentary nuts or the Ghibli fans. It’s a slow one, and there isn’t that much to really invest in, but there is a big crowd for this stuff.
HOTD - Despite the annoyingly over-the-top sexualization of characters, this show is the perfect zombie show full of energy and memorability. For those who love zombie movies, or thrillers, or survival-based media, or even the glorious Kurosaki Maon.
Rainbow: Nisha Rokubou no Shichinin - A really nice show for the other side of the thriller spectrum. Zombies too silly? Have a dark look at the imprisonment of a great cast. It works well with history buffs or psychologists too~
School Days - We all know this show. It’s the perfect opposite to Clannad. A romance drama, turned up to 11. Lots of people don’t like the show, but it IS a good gateway show, simply because of how different it is to what is expected.
Sola - The good one before Sora no Method. A nice fantasy romance, but the fantasy isn’t too important. People with an appreciation of nature will like this one, however it can serve a similar purpose to School Days. Different enough to be memorable.
Mobile Suit Gundam 00 - Gundam is a big name. It’s something for collectors, for mech fans, for action fans, and for drama fans. 00 is pretty much the pinnacle of the franchise from the perspective of a modern western audience. The more tolerant or aged people might prefer one of the older titles in the franchise though.
Zegapain - This show is one of my all-time favorites. I don’t like the mech genre, but this is still one of my favorites. Anyone with a love of scifi, or of computers, or with an upbringing revolving around 90s Saturday morning cartoons, will love this show. Oh, and what better way to introduce HanaKana? This is her at her best, and she wasn’t even experienced then.
Higurashi - Horror and mystery fans rejoice. Similar in vain to School Days in that it’s more than expected, but for a different audience. I’ve seen 6 year olds love this show, and I’ve seen 40 year olds love this show. The animation is bad, the voice acting is iffy, and the story is convoluted until you put in enough time… but you don’t notice any of those things with your first anime. It’s the best time to watch Higurashi, because it’s flaws won’t be apparent.
Mushishi - Someone already interested in Japanese culture? Someone big on nature? Someone who likes to think about how everyone they see has a story to tell. Follow this up with Kino no Tabi or Kaiba, and you’ve got them hooked.
AnoHana - Similar to Clannad, but with more focus on friendship. Show this to the guy who is stuck reminiscing his childhood, or those who are just about to leave their old life behind. A midlife crisis might prime you for this too.
Black Lagoon - For the 80s guys and the brooding teens.Seriously though, it has a wide appeal. Action story, about smuggling and pirating, with a strong good looking female taking the lead? May as well be the non-scifi Alien of anime.
Ef - This is pretty much the safe ground between Clannad and Anohana. It’s focused on current affairs, and on friendship, but family isn’t too important. It shares the same audience as the two, but it’ll appeal to writers too. It’s nice for Christmas as well.
Madoka - I hate this show, but I don’t hate the fans, so I accept it as a gateway anime! Those who grew up with Sailor Moon or CCS, or any girly cartoon show, will probably like this. It also follows the trend in that it’s different enough from the norm to be memorable. Don’t give this to someone who doesn’t like magical girls though. It’s boring.
If their first wasn’t Clannad, don’t rush them to it. Show them the sights, and lead them to the genre. Anyone looking for a romance drama will find Clannad. I say Clannad, because Kanon isn’t as welcoming, and the first season of Litbus is even worse than Clannad’s.
Naturally after finishing a story you get caught with the “I want to know more” bug, and from there people will discover VNs, and then Key.
The big anime work too. I got a few friends into anime via Naruto, and they all branched out into watching totally different genres. One one side there was Elfen Lied, and Daily Lives the other.
For some strange reason? That seems perfectly normal to me. I sat through the Internet hype of Code Geass R2, and didn’t watch the show until this year.
Sure a show might be good, but I’ve heard it’s name so much that I just don’t care about it anymore. When I eventually run out of average or better anime, I’ll give it a try.