Color management is an annoyance that I've recently been learning about; it is not completely accurate to say that just because your monitor can only display sRGB that it's meaningless for your photos to be edited in the AdobeRGB or ProPhotoRGB space. What is actually happening is that Lightroom is translating colors from ProPhotoRGB into the sRGB space that your monitor can display. It does a bunch of fancy math (I think maybe some matrix algebra? I'm not positive, though, maybe somebody can correct me) to perform this translation -- thus, what you see in Lightroom is not your image as it appears in ProPhotoRGB or in sRGB, you are seeing an interpretation of ProPhotoRGB space in sRGB that tries to be as faithful as possible to what the image would look like on a device capable of displaying ProPhotoRGB.

When you export your photos from LR, you have the option of choosing what color space you want to use for the exported photo (you can choose sRGB, AdobeRGB, and ProPhotoRGB, among others). When LR does this, it first converts the photo into the chosen color space, and embeds information into the JPEG file describing the color space (these things are called ICC profiles). Now, when you open the JPEG in some other program, if that program is able to understand the embedded color space information, it can perform the same math that LR does to convert the file into your monitor's color space, and it should appear the same (or at least similar to) LR. If the program you open it in can interpret this embedded color space information, we say that it's a color-managed application.

The problem is that a lot of applications are not color-managed. Windows Photo Viewer may or may not be (I've read competing statements, but in any case it doesn't seem to work as well as LR); Firefox only supports old versions of ICC profiles, Safari and IE are, and Chrome is not. So if you open up your image in one of those applications that doesn't support color profiles, or doesn't support them well, your image is going to look bad because the proper color translation isn't being performed.

There's a really nice three-part series on color management here. You can also check out whether the device you're displaying supports the appropriate ICC color profiles using this test image. One other really neat feature of Photoshop CS5 (and maybe other editors too, I don't know) is that it will actually show you what parts of your image won't translate color spaces well; if you press Ctrl+Shift+Y, or go to View->Gamut Warning, it will highlight in grey the colors of the open image that don't exist in the target color space. I've found this to be somewhat useful.