In a word, wow! I've had a DSLR about 6 months, but have taken nearly 10,000 exposures (of which I've probably kept 10%). Once I moved to shooting in RAW (which if you're not doing, you don't really need Lightroom), my workflow began to take quite a while. I'd do an initial review of my images using Picassa, to get rid of the ones not worth processing (but which looked ok on the camera LCD). I'd then use the Photoshop Elements RAW editor to sort out white balance and exposure. This works fine, but it's a fairly slow process and a bit of a clunky interface. I'd then export to Elements, do my cropping and effects, and then batch save as JPEGs. Lightroom has been an absolute revalation. It automatically imports the images (being really flexible about file locations and names etc), and then quickly lets you review and reject images. This step alone is MILES quicker than my previous process. The white balance and exposure settings are much more comprehensive than the RAW editor in Elements (I can't compare against full Photoshop) and it has some brilliant pre-sets (such as high contrast B&W, cold tone) which very qickly give me results which are 95% what I want, and I can then tweak. The tools for cropping etc are very good, and there are several image maipulation tools built in which make me think I won't need to use Elements post-processing functionality much in future.
Downsides? I haven't really found any to be honest. It's not cheap, but do look at Adobe's educational licensing options (eg do you have kids at home who may qualify?). There's no real documentation, but if you've used a RAW editor before, it's fairly straightforward. I recommend the Scott Kelby guide to get the most out of the software though. In terms of processing, I see some reviewers have a problem with the amount of memory etc it needs. I have a 2 year old laptop, and processing in lightroom is much faster than in Picassa & Elements. Finally, if you have full photoshop, then you need to read some reviews to see how it compares to the RAW editor in there, as I can't give an opinion on that (as I've not used it).
In summary, this has cut my workflow time by around 65%, and gives me better looking results. That to me, is well worth the money. Highly recommended.