I have a section of my closet reserved for puzzles and related things, and usually my main 3x3x3 and the cubes I'm concentrating on that moment are on the computer desk in the living room
I've been cubing for so long, I just scatter them across my room. My main cubes are usually just scattered on my table and what not. The others are kept in a shoe box, unattained. I've never been a high maintenance person anyway.
My computer desk has a few shelves integrated into it, to the right of me.
The bottom shelf is entirely dedicated to all things puzzle related, and everything is neatly propped up on display. Also, the shelf has two red cold cathode (neon type) lamps, which makes it look awesome!
My mains are in a corner on the settee by where I put my laptop when I use it; my old Rubik's storebought and my broken Meffert's pyraminx on my desk, and the old toothbrush I use to clean my Zhanchi is usually kept in my pen drawer.
I store my puzzles, stickers and tools in a transparent plastic drawer unit from Wal-Mart. I like it because the big drawers are deep enough to store even the biggest puzzles (I have a Teraminx and a couple of Tuttminx). I put a towel in the bottom of the drawers so the puzzles won't slide and hit each other. Of course, I have a selection of puzzles on the corner of my desk (I see 8 there now).