How can I install iTunes in such a way that it can't put any "hooks" or helper programs on my computer?

Ed Bot had written an article on how you install iTunes 10 without any helper programs. It's a long 3-page post, but to summarize

• When you run the iTunes setup program, it unpacks six Windows Installer packages and a master setup program, which then installs nearly 300MB of program and support files, a kernel-mode CD/DVD-burning driver, multiple system services, and a bunch of browser plugins. It configures two “helper” programs to start automatically every time you start your PC
• To trim down, the master setup program is first extracted using 7-zip / IZArc and each individual setup program can be run

Performing a selective iTunes install involves three steps:

1. Extract the installer files you need to a local folder.

2. Run the installers with the proper command-line switches.

3. Prevent Apple Software Update from undoing your careful work later.

I would recommend you read the full article and customize it as you like.

I too am not a fan of iTunes. However, ever since I got a free iPod touch and now have an iPhone 4, I need iTunes to sync all my data. I use 7zip to extract the installer I download directly from Apple.

1. Then, I delete the Quicktime and AppleSoftwareUpdate msi installers.

2. I then install the ApplicationSupport first, followed by MobileDeviceSupport, and then Bonjour.

3. I install iTunes by going into an administrator privileged command prompt and navigate to the directory with the iTunes installer. I use the following command:

    *msiexec.exe /i iTunes64.msi /quiet*
   

And iTunes installs without Quicktime and software update. Of course you need quicktime for iTunes, so I use the latest version of QTLite which works very well with iTunes.

You can delete bonjour and MobileDevice support if you will never use things like Home sharing or zero-config networking and if you do not have an iDevice.

This may feel like overkill, if it's only for iTunes, but what I personally do is run another copy of Windows in a virtual machine, for installing any questionable software (which includes iTunes, in my opinion). Especially if you download a lot of freeware applications (or pirate software, God forbid), it's a good way to keep your workstation clean.