It's definitely possible to dress up without looking like a stiff in a suit. Get a decent button down from somewhere like J Crew or Banana Republic, a pair of nice, dark jeans (or khakis) and some dark leather shoes. The key take-away is

  a suit doesn't necessarily = well-dressed
  no suit doesn't necessarily = not well-dressed

Think of your typical office drone (like the guys in Office Space) - they're in crappy suits and don't look that good. Likewise, some of the best-dressed people hardly ever wear strict "suits."

But, I do agree with the poster below: If a company balks because you overdressed for your interview it's their problem, not yours.