There are several articles with suggestions what to do with a Raspberry Pi but many of them are only ideas without any instructions.
Is there a directory of projects that actually have been realized with list of required parts and steps how to do it with your own device?
For example a collection similar to "Thingiverse" or "Solderpad" would be great!
Project directories with instructions:
RaspberryPi.org's official resources, mostly directed at students and teachers, but of very high quality.
Instructables' Raspberry Pi channel. They have A LOT of projects.
Hackaday.io's curated list for Raspberry Pi. You'll actually find a lot more by doing a search for "Raspberry Pi". Not all have instructions, but many are really cool.
Hackster.io's Raspberry Pi hub. They have fewer projects than the previous two but all have instructions and parts required.
Adafruit's Raspberry Pi section is brilliant and full of high quality tutorials. An open search for "Raspberry Pi" brings even more.
Other sources for instructions and inspiration:
You can run a YouTube search for Raspberry Pi (If you do this regularly you will want to sort by date uploaded). This will turn up a lot of breadboard experiments, including hooking up an LCD Screen. Be sure to check the comments section for build details.
You can subscribe to the Raspberry Pi sub Redddit. Anything new an interesting will surely show up there.
You can check out Mag Pi magazine. they have a few build and coding tutorials.
You can also browse the Raspberry Pi forums, especially the projects section, and the Projects, Guides & Tutorials section of the R-Pi Hub at elinux.
You can search github and github gists for Raspberry Pi.
You can subscribe to tumblr's raspberry pi tag.
You can also set up a Google alert to email you once a day with a list of resources the Googlebot has found while indexing the web.
You can also join the Raspberry Pi community on Google+.
You can like the Raspberry Pi Facebook page.
You can search for Raspberry Pi on Pinterest
Finally you can check out the Raspberry Pi User Guide that was recently announced.
I realize this may not be the answer you were hoping for, but as I said the Pi is new and it will take some time to develop a community and ecosystem around it.
Don't forget that you can always ask specific questions here as well.
UPDATE 8/23/2015 OP's question was specifically about directories of projects that contain required parts and instructions. There are new ones that did not exist 2 years ago, so I've put them at the top of the list since they best answer the question. I've also updated resources that have moved or closed. (ben)
Mike Cook is going through his ~30 year computer/interfacing article experience, and modifying them for the Raspberry Pi: The Raspberry Pi Punnet.
I'm running a project to run a WordPress-powered web site from a Raspberry Pi web server. I've installed Apache PHP MySQL and written tutorials throughout my project's progress.
Take a look over at my project homepage.
I've asked myself the same question and in the past 2 weeks I have found a few sites with some simple projects. Some were already mentioned above, like Adafruit Learning Systems, or the pretty big collection of projects on the RPi Forum. The eLinux list is probably the biggest collection of links to tutorials and projects I've found so far.
http://www.raspberryconnect.com has a user projects area set out by category with the aim of being a directory of raspberry pi projects, websites and blogs. Anybody with a Raspberry Pi project or website can add their own content.
A small company called PiBorg are producing some interesting GPIO projects, very early days but looks like there will be some interesting stuff.
Here is how to automate your home using Siri and Raspberry PiHome Automation
