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The Web standards and their support in browsers have really improved. It is now time to drop the old proprietary and binary formats and replace them with open, standard technologies.

PDF

It is a proprietary binary format. You can't open it without a third-party plugin and you can't construct or process it without special libraries or applications.
Does not look very portable after all. So why would you ever publish something on the Web in PDF? Right, it is supposed to give precise control over the layout of the document and make it print nicely. But have you checked lately what (X)HTML and CSS are capable of these days? And if you'll need graphics or formulas in your content, there is SVG and MathML. Drop PDF and go for nice and rich webages.

Microsoft Office files

Very much the same as for PDF. But if you really need to publish in some office-suite format, choose OpenDocument (ODF), which is an XML-based standard.

Flash

Like PDF, Flash is proprietary, binary, requires a plugin to play it and special software to build it. Furthermore, it breaks accessibility and navigation, is hard to use on non-Microsoft platforms, and is not indexed by search engines.
Drop Flash and switch to SVG, which is an XML-based standard, supports animations and has a programming interface. Consider SMIL as well.

Raster images

Where possible, replace your raster drawings and graphics with SVG. That will make them scalable and improve accessibility, among other things. And for other kinds of pictures, at least consider switching from GIF to PNG, which supports transparency and a wider range of color depths and is a non-proprietary standard.