Agreed
Of their more well known series, I think this would be a good start for newcomers (in order of showing)
Magic Knights Rayearth
Ehh, maybe skip that one, unless they're like 5 y/o... ;o)
Go with Sailor Moon / Ronin Warriors.
I guess I should weigh in with MY list now too, eh? Will try to pick out fairly obvious stuff.
Here goes, from a forum n00b and an anime semi-n00b (almost, but not quite)... Only in a minimal order:
Dragonball Z (Dragonball for some of the younger-uns)
Ronin Warriors (Ha, like anyone can find a legit copy at a reasonable price! They need to reprint this.)
Saint Seiya
Sailor Moon
Yu-Yu Hakusho
Inu-Yasha
Rurouni Kenshin
Evangelion
Many things Gundam (I've seen Wing, which I liked and G, which I also sort-of liked, still working on the rest)
Robotech Protoculture collection (heh, okay, too much...)
Ghost in the Shell + SAC (SAC's gone Anime Legends, so it's cheap enough these days.)
Outlaw Star (as a few people have reminded)
Escaflowne
Ninja Scroll
Wolf's Rain
Witch Hunter Robin
Slayers
Most Miyazaki movies (Miyazaki's largely canon right? Spirited Away, Howl's Moving Castle, etc.)
Akira
Princess Mononoke
Tenchi (debatably; not a huge fan, but it's popular and been done to death in several series, sequels and spin-offs, so I guess it qualifies, eh? Much like DB, DBZ, DBGT, Sailor Moon, Pokemon, etc.)
Naruto (debatably; the debate's been done to death on many forums, or so I hear. Listed sinec most people should have at least heard of it / know what it's all about, even if they despise it.)
Pokemon (would follow from the prior logic on Naruto, I guess? Maybe not something to go out of your way to screen for someone.)
Personally, I think Legend of Himiko and Twelve Kingdoms should make the list. Liked both. Good animation, decent storylines in both.
Sorry if a few of these were on the list already... OP said obvious / n00b / well-traveled stuff. As others have said, not all of these are maybe right for everyone. Just fairly popular. Might I repeat we should lobby to have Bandai reprint Ronin Warriors?
Well, I enjoyed it anyway. Hard to find good samurai / dark fantasy (well, okay maybe not; just reminiscing about the old school Toonami days).