According to wikipedia, by a theorem of Henderson '69, infinite-dimensional Frechet Manifolds embed as open subspaces of Hilbert Space. They need to be seperable & metric. They are generalisations of Banach Manifolds, so they too have the same property.

Michor & Krigel, say 'this does not make them [Banach Manifolds] interesting [enough]' in The convenient setting of Global Analysis,

What are the other directions to take, when looking for interesting infinite-dimensional manifolds, (besides the one Michor/Kriegel outline in their book). And has a canonical choice begun to establish itself yet?

ifa Fréchet manifold is separable and metrizablethenit embeds as an open subset into $\ell_2$. Finally, what exactly is the difference between the present question and your earlier question mathoverflow.net/questions/90656? – Martin Dec 5 '12 at 20:46