There are quite a few alternatives, depending somewhat on what you're after.

Workflow software

Personally, I like Bibble quite a bit. If memory serves, the Pro version is around the same price as LR, but the Lite version is quite a bit less expensive. One warning: while Bibble works well, they do have a history of being rather late delivering new versions (e.g., Bibble 5 was promised for something like 2 years before being delivered). For noise reduction, Bibble uses a version of Noise Ninja, which is (quite rightly, IMO) considered one of the best noise reduction programs available (though there are certainly others that are competitive).

Note: Bibble discontinued in favour of Corel AfterShot Pro

Raw Therapee is an open-source raw converter with decent noise reduction and a heavy emphasis on demosaicing algorithms to extract as as possible from any given raw data file. The goal here is more to get the most out of good pictures than reduce noise (and such) to save those that aren't so good.

SilkyPix Developer Studio Has pretty good noise reduction as well -- depending on the situation and picture involved, it's sometimes better than Noise Ninja (though other times it's not quite as good).

LightZone is yet another. Basically all the same kinds of features, as most of the others. I haven't used it enough to really comment on it in any detail though. Their big brag is their "Relight" -- one-click fix of exposure, contrast, etc. It seems to work reasonably well -- for one example, in the same league with Athentech Perfectly Clear (Ps Plugin, also included in Bibble Pro). Their noise reduction appears usable but doesn't seem to be anything special.

Aperture is Apple's workflow software. Given that it's from Apple, it's no surprise that it only runs under OS/X, so if you're a Windows user, you might as well move on to the next item. If you do use a Mac, it should probably be the first one you test. You might easily not bother looking at any others -- Aperture is easily competitive with (or, in the estimation of many Apple fans, clearly better than) anything else on the market.

editing software

These are much more like Photoshop than Lightroom.

Photoshop Elements was originally developed as an update to Photoshop LE. The first couple of versions were kind of lame (missing some features I'd consider truly crucial), but more recently it's not too bad. This is one, however, that pays to read some of the "tips and tricks" kind of papers/books/magazine articles -- quite a bit of what you can do is semi-hidden, so if you just use it for what's obvious, you see something much more limited than it really is -- though I haven't used the most recent version, so this may not be (as) true anymore.

PaintShop Pro X3 is another that started life (long before Corel bought it) as (at least IMO) a fairly worthless wannabe program you'd run across at Walmart for $19.95, but over the years they put in a lot of time and effort, and turned it into a serious photo editing program. I haven't used it a lot (actually, I haven't used X3 at all -- my most recent use was of X2) but it seems amazingly close to the capabilities of Ps even though the price is about the same as Ps Elements. The obvious advantage of Photoshop is support for roughly 10 zillion add-ons, plug-ins, presets, etc.