I think I have the opposite problem. At the risk of sounding like a *really* boring person (from a fashion perspective, anyway), almost everything I own is a basic! I'm trying to imagine the statement pieces I own, and I'm drawing a blank.
In fact, the most statement-y things about me are (a) my hair - it's pretty modern and at it's current length, somewhat rad in my circles; and (b) the absence of statements in my clothing choices. My colleagues will probably say that I'm more well-dressed than the norm for our profession, but that's because I try to put some thought and creativity into what I wear and how I look (OK, on most days) in a profession that, arguably, takes pride in not caring about looks.
It's hard not to be disappointed at the basic nature of my wardrobe; at the same time, identifying the items of clothing that do count as basics for me has been a style journey. Moving to a new country 12 years ago turned my definition of "basic" topsy turvy (given my current lifestyle choices, salwar kamizes are now "optional", "special occasion" pieces rather than everyday wear, for example). Finishing graduate school and starting work in a new (academic) profession and dressing a body that is considerably different in my 40s have added interesting twists and turns to the evolution of my style.
Anyhow, I think I'm arriving at a place where I'm settling on how I want to look - modern, classic, and "pared down" (to use Sunita's term for my style). And, finally, I think my closet is getting to a place where it is well-stocked with *my* basics.
My challenge now is one of figuring out how to add character to my outfits -- right now, II fall too easily into the trap of looking boring or, worse, frumpy, when I am wearing these basics. I have often toyed with the idea of mixing in accessories (scarves, jewelry) that'll both point back to my ethnic origins and add some character to my outfits but I don't yet know how to do it in a way that's classic and understated. Right now, it usually feels a little too much like I'm trying too hard, and that doesn't feel right.
Sorry about the over-long (and, um, navel-gazing) response, but your post really sparked some serious introspection here. Thanks for getting me started thinking about this (Suz's posts over the last few days have really helped too). I'm looking forward to the next step of my style journey here on YLF.