I don't think grey counts as a colour really - it's a neutral. Personally I prefer grey and white as neutrals to beige and cream - I think it's really hard to have, say, sand and grey tones together without your house looking like someone vomited all over it, so you either go warm neutrals (beiges and creams) or cool (greys and whites) with whatever other, brighter colours you like, or you just go for white with other colours.
Neutrals don't really go in and out of fashion, I don't think, although there was that massive thing for beige a while back, eg travertine bathrooms, and chocolate brown was wildly fashionable about 10 years ago, but I don't see that as a neutral colour. Apparently gold and navy are coming in, but they'll date terribly, and aren't neutral at all.
I think if you want a non-beige, non-grey, non-white that won't date, I'd go for a mushroomy neutral that is basically a warm, but not yellowy, grey, and quite light in tone, which will work with blues, purples, most greens and some yellows, and mix that with mostly white and some other colours of your choice that you can easily change when you're tired of them.