I'm almost too embarrassed to post this. It's so simple and obvious that I now assume everyone has a similar mechanism in place. But, if your Photoshop-to-web workflow is like mine, you'll really appreciate this.
My normal process for working on an HTML/CSS build is to select the layer(s) and/or Smart Objects I want to create a new image from, create a new file with dimensions large enough (plus some extra) for them, drag the layers over to the new file, use the PS trim command to remove all excess whitespace (or transparent pixels), then Save for Web. This is incredible tedious and even though I've always known I should automate this somehow, I've never bothered.
But now I've finally put together a super-simple Photoshop action that will do all of this for me. All you have to do is select the layers you want, hit F1, and you're presented with the Save for Web window.
If you want to give it a try, you can download it here. There's not much to it, so I'm assuming it'll work in most recent versions of Photoshop (FWIW, it was created in CS5). If you want to change the function key, you do that by clicking the menu dropdown on the Actions panel and select Action Options.
Update: I've created a public Github repo for this. Feel free to fork and tweak as desired. If you come up with any other useful actions to add, drop me a line.