1. Plot . I have literally seen a hell of a lot of anime with poor plot decisions and very bad story choices. Completely decimates a series and makes the viewer never trust that studio again.
2. Music / Score . This is just essential to any anime period. Great music sets the tone for what is to come. [Such examples are Elfen Lied, Chrno Crusade, Hellsing.]
3. Character Development . If you cannot associate with the characters, what is the point of continuing to watch the anime? Great character development leads to HUGE fan followings. [Case in point, Great Teacher Onizuka, Full Metal Alchemist, Get Backers.]
4. Artwork . The art does not have to be utterly spectacular, but some attention to detail, some incorporation of 3D elements or even painted elements, traditional hand drawn is always a major plus and a major draw for me. [Prime examples, Hellsing vs Hellsing OVA vs Hellsing OVA Blu Ray. Look up the different pictures available for each of these online, and you will see exactly the type of progression and artistic addition I truly love.]