A naked Raspberry Pi costs $35. Add an enclosure and shipping, it will be closer to $60. That doesn't include storage.
Time Capsule contains a 2TB hard disk. The same WD drive retails for $170 at Amazon.
That brings our total to $230, for a product that doesn't work nearly as well as a real Time Capsule and for which you won't receive service and support from Apple.
Or you can just buy a Time Capsule for $299: http://store.apple.com/us/product/MD032/time-capsule-2tb
However, I've also run a linux/netatalk box, back in the snow-leopard days. It did "work", but things would get screwed up for me if I ever closed my laptop whenever a backup was in progress.
I ended up using an airport extreme for time-machine backups. It works well. I have it connected to a Sabio raid box.
I don't think apple advertises that the extreme works for time-machine, but it's basically plug-n-play type setup. No hackery required. Just an external disk with USB connectivity.
However Time Capsules run hot and have a nasty habit of burning out every two years or so. I presume the Pi + external drive would run cooler and have a much longer life.
Time Capsule Memorial Register:
Time Capsule is a very convenient way to use Time Machine, and it works great until it dies. Judging from the other comments, that's the difference with the Raspberry solution, which apparently isn't very reliable and doesn't allow for HFS+ with Journaling.
If you deal shop, you can get the price down:.
 $40 Raspberry Pi - Model B, because that's all that's available (includes $5 shipping)
 $10 Enclosure (some DIY required)
 $116 WD 2TB Hard Drive (selected WD because that is [apparently] what Apple uses)
The case I spec'd is extremely DIY as well. If you went with something nicer, you'd spend more as well. It's kind of hard to justify a crappy case when you're comparing to a Time Capsule.
So if you add in $20 for a HDD price not-so-on-sale and $10 for a nicer case (Adafruit is decent), you're looking at $196, which is edging up toward the cost of a Time Capsule, and that's not factoring in time for configuration.
The whole point here is that you don't do projects like this to save money. You do projects like this for the fun and learning experience, or to have greater control/flexibility. If you go in to this project to save money, then I think you're barking up the wrong tree.
1 - Pick a vendor any vendor (pricing is standard)
2 - http://blujay.com/item/Black-Electronic-Project-Box-100-x-60...
3 - http://www.amazon.com/Western-Digital-3-5-Inch-Internal-Desk...
That was where I was leading it, yeah. Attacking it on a price basis just seems weird to me.
The title of the article is "Time Capsule for $25", so apparently the author thought the price is the main selling point. The actual price is way higher, he set himself up for someone to point that out.
That drive is listed as $169 MSRP at Amazon. 
By the way, my first generation Time Capsule has a 500GB Seagate Barracuda ES, which used to retail for over $300.
 From my Amazon order history: http://i.imgur.com/lYYlR.png
I suspect some of this is due to limitations in netatalk's AFP implementation, but I've never compared to a proper Time Capsule
As for people saying that the complete setup is almost as expensive as an actual TimeCapsule - yes,but then I had a spare 500GB drive laying around,and had no special use for my Raspberry Pi. Thanks to this both of them are used on a daily basis.