Anime content definitely comes in tiers of quality. It's just like any other entertainment medium out there. When people talk about movies, video games, TV shows and music, there are certain bits of content that people deem as 'must see'. These are the projects that any respectable fan of whatever it may be must expose themselves to. If you don't, you're simply missing out on the best of what that form of entertainment has to offer.
Anime is no exception to this rule. There are certainly anime TV series' and films that a majority of fans would consider to be must-see. These are the high watermarks for anime in general that help to showcase what the medium brings to the table. They transcend the norm to become something that is appreciated by circles that don't usually appreciate anime.
I know I'm going to miss a few anime features, but I'm going to do my best to put together a short list of anime that is considered to be must-see. I'm not talking about anime that anime fans consider to be required viewing, but instead, anime features that even traditional film/TV buffs consider important.
Ghost in the Shell
Neon Genesis Evangelion
At least one Miyazaki film
Grave of the Fireflies
Now out of that collection, what features have you not seen? I'm ashamed to admit that I've never seen Grave of the Fireflies, but I plan on changing that soon. Hopefully I won't get too harassed for not having seen it yet!