As long as the design doesn't get in my way, I'm good. That means: no splashscreen, Flash or otherwise; no soundtrack; no "dancing baloney" (technical term); no more than two plugins needed to use the site for its primary purpose, and those should not be mandatory; no crowding/judicious use of whitespace; basic usability in place (readable font face, legible font size, sufficient contrast for ease of scannability, sufficient spacing, et cetera); and solid information architecture. Don't make me try to guess where to find things or how to navigate the site.
Other than that - designers, start your engines. Floral, simple lines, boxes, curves, curlicues, racing stripes, grunge, cartoonesque, trompe l'oeil, pixellated, whatever.