UPDATE [Jan 2019]: Pantone now maintains their own web-conversion/lookup tool. I guess enough people were searching for—and maybe complaining about the lack of—a solution, they finally caved and gave it to us ;)
If you're like me, you often have to convert colors between CMYK Process colors & Pantone Spot colors for print, and RGB & Hex values for web stuff. Sometimes a client will provide one or the other, and expect that everything will look exactly the same whether the graphic is on paper, or illuminated from behind on a monitor. Without going into why this is impossible, let's look at a few ways we can make a go at converting the colors as accurately as possible.
A quick Google search returned a few sites that have a Pantone to RGB conversion chart (although not as many as you'd think - more on that later). eDigita has one, for example. There's also a tool by Ruig that allows you to enter a value in Pantone, Hex, or RGB and it generates the corresponding values. This has the added advantage of not having to scroll through a long page of color values, but interestingly, this tool and the eDigita table produce different results!
Searching around some more, it seems that Pantone has actually been going around shutting sites down for having such tools!! Reed Design and seoconsultants.com both mention this. If you ask me, this is a bad move by Pantone - making your proprietary color scheme harder to use? It may be because they have their own tool - myPantone Palettes. But wait - you'd think Pantone's tool must render the other tools moot, but it doesn't. Why?
Pantone forces you to become a member of their "community" in order to download the software. Furthermore, even though the software is free, the Pantone color books must be purchased! And the form you have to fill out in order to "join" is huge - they're not shy about doing some market research while they have you by the color-palette-kahonas. And lastly, upon looking at the manual, the "tool" looks scary enough to just avoid entirely.
So, we're back to square one - a variety of online tools that hopefully will dodge the legal bullet long enough to help us with a bit of color-matching. Hope this round-up helps.