I know that through iTunes you can store images, audio etc. on your iPhone. But is it possible to access the iPhone and store any kind of files for later retrieval, much like a memory stick?
There's an app called Phone Disk that seems to do exactly what you need. The one downside is that it needs to be installed on the host computer to work.
Sure, take a look at the iOS app Air Sharing. It makes a storage area accessible over Wi-Fi via WebDAV. It also allows you to view the contents of some file types on the device itself (for as far as there are built-in viewers).
Alternatively, you can jailbreak and store files directly in the iPhone's memory. Use SCP over WiFi, or connect the USB and use iPhoneBrowser.
A simple technique is to leverage File sharing feature available for iOS apps.
Instructions for the same can be found in the Apple Support article, About File Sharing on iPhone, iPad, and iPod touch.