First Anime I watched were DBZ and Pokemon, but I wouldn't say those were the ones which got me into Anime. I think it was Inu Yasha that made me buy an Anime magazine. The first DVD I finally bought was Love Hina.
It's either Dragonball Z or Pokemon for older partisans in anime, any others make those people questionable as to what generation of media they are a part of.
*Part of the Pokemon, Digimon, DBZ, Cowboy Bebop, Inuyasha, Minor Final Fantasy Generation, etc.*
The generation which is older before that would be things such as Monster Rancher, Sailor Moon and more Final Fantasy.
The cause of this is a era gap even between a couple of years. Most of those that are around the ages of 15 and under are the Naruto, Bleach, and minor FMA, etc. people. The ones just above them in age, just about 16 1/2 and older, have more FMA, and have been exposed to the generation I just explained and have already grown tired of Naruto, Bleach, Big name titles, etc. Those who still follow them are usually just occasional viewers, not enthusiasts like most in the age 15 range.
Pokémon was the first anime I ever saw, and which essentially got me liking anime. I didn't realise it was an anime at the time because I was 9 years old, and 9 year olds tend not to ask questions if they like it.