How can I make Adobe Lightroom run faster on an older Windows PC?

Something that hasn't been mentioned yet: in 'Catalog Settings' turn off 'Automatically write changes into XMP'. This will prevent LR from automatically dumping its catalog metadata, keywords, rating, labels and develop settings back to your photo files. By doing so you will reduce the number of disk operations performed by LR. You can still write your metadata back manually, as I describe in this other question.

I have 8GB of RAM and I process 21MP RAW files out of a Canon 5DMII. Increasing disk performance is how I made it run faster. I replaced a pair of fairly zippy Hitachi SATA 15,000 RPM drives by a pair of 160GB Intel X25G2 SSD. Be careful with your choice of SSD drives, they are not born equal. Most of them read really fast, but many are slow on write. Pair your SSD with a modern operating system like Windows 7, one that supports the TRIM command.

What should you put on a SSD and what should you leave on a standard drive? Opinions differ, but here is what I would recommend:

• your LR catalog file (Lightroom 3 Catalog.lrcat), which is where LR stores its metadata, keywords, rating, labels and develop settings
• your Previews directory (Lightroom 3 Catalog Previews.lrdata), which is where LR stores intermediate representation of your photos for faster viewing (1:1, low res, thumbnails, etc)
• your Adobe Camera RAW Cache (ACR Cache)
• your RAW files, or at least a subset of them

What is the Camera RAW Cache? Quoting Jeff Schewe via Luminous Landscape Forum

Every time you open an image in Camera Raw the full resolution of the image must be loaded into Camera Raw… as you can imagine, this can be pretty processor intensive… the Camera Raw cache will cache recently opened images to make re-opening them faster. There’s a preference limit to determine the size and the cache will remain constant in size by flushing out older cache files when newer images are loaded into Camera Raw.

You can change the default location of your catalog, previews and Camera RAW Cache from the Preferences and group them on the same SSD. I would definitely recommend increasing the size of your ACR Cache, if you can afford it.

RAW files are big. You don't need to have all of them on a SSD, but what about the past 6 months worth of photos? Move older photos back to a standard drive every month or so (do it from LR of course).

Do you need to put LR or the whole Operating System on a SSD? If you can, sure, it will start faster and feel a bit more responsive, but I don't think it's critical. If you don't have a lot of RAM though, try to put your page file and TEMP directories on the SSD.

Should you go RAID0? I really recommend against it, unless you have really strong backup habits and monitor your RAID controller regularly. Remember, RAID0 uses 2 drives: if one dies, you lose the data on both. Don't risk it. I personally like RAID1 a lot for this very reason and from past experience.

Finally, you will "feel" LR run faster if you let it generate your 1:1 photo previews during import. I usually do something else during import anyway, run some errands or whatnot. In any case LR has to generate your 1:1 previews sooner or later when you go to the Develop module, right? So you might as well let this happen during import.