As a developer, I've learned a heck of a lot from the global community and I believe like any community, you need to participate and contribute.
I've worked on several small projects that I want to offer up for free, but I want them to actually be used.
For the sincerity of this post, I am not going to promote them here.
What are some good ways to offer a free resource like a widget that does x,y, and z, for free. With an honest-to-god intent to just contribute?
make a screencast showing how you made the software - other programmers will watch the video and may in-turn blog about it
i'm sure you'll get better suggestions than that though, good luck
Assuming it's open source, add to freshmeat for example to help people find it.
Write really good documentation, with examples etc. There's load of code out there which is lacking documentation making it pretty useless no matter how good the code is.
Make it easy for people to report bugs, suggest features, etc.