where I can find very small and clear icons that I can use in a personal (non-commercial) project?
Generally a place where I start is
I'm sure you'll recognize most of those icons.
Most times after the details of the project are settled and the general look&feel needs to get right I switch to custom ones, though. mainly because of differing colors schemes.
As leugim said, famfamfam is very good.
Smashing also puts together links to collections every now and then: http://www.smashingmagazine.com/2008/07/02/55-free-high-quality-icon-sets/
The linked article also has links to older compilations of icon sets that they've put together.
Similar to famfam silks, I think the colors are a little nicer.
They are not pixel icons, but you can convert the vectors to pixels. Very clear icons, all under creative commons and they are almost uncountable ;).
Font Awesome has great icons and is easy to use.
Yuskue Kamiyame's Fugue Icons is a very good set that I use often. There are almost 3,500 icons in the set, so you are bound to find something that can fit in with what you need.
The sources are also provided if you would like to tweak the icons.
Take a look here:
Icon set includes both 16 and 32 pixel versions of icons.