We report on the resolution limits of Electron Beam Lithography (EBL) in the conventional polymethylmethacrylate (PMMA) organic resist. We show that resolution can be pushed below 10 nm for isolated features and how dense arrays of periodic structures can be fabricated at a pitch of 30 nm, leading to a density close to 700 Gbit/in(2). We show that intrinsic resolution of the writing in the resist is as small as 3 to 5 nm at high incident electron energy, and that practical resolution is limited by the development of the resist after exposure and by pattern transfer. We present the results of our optimized process for reproducible fabrication of sub-10 nm lines by lift-off and 30-nm pitch pillar arrays by lift-off and reactive ion etching (RIE). We also present some applications of these nanostructures for the fabrication of very high density molds for nano-imprint lithography (NIL) and for the fabrication of Multiple Tunnel Junction devices that can be used for single electron device applications or for the connection of small molecules.