Acrobat 8 displays side-by-side pages differently than previous versions of Acrobat. When you choose View>Page Display>Two-Up, Acrobat 8 displays two pages side by side, but with odd pages (including the cover) on the left and even pages on the right. This prevents two-page spreads from displaying as they appear in a print document. To change this, choose View>Page Display>Show Cover Page During Two-Up.
Of course, if you are creating a PDF to distribute to others, you can control the initial view of the document. Choose File > Properties. Click on the Initial View tab, and choose Two-Up (Cover Page) for the Page Layout. Click the OK button, and save the PDF.