I volunteer at an organization which provides services to the homeless. At one location we stock a warehouse of clothing, household items, toiletries, and school supplies. Caseworkers at other locations need to know what we have in stock. Promoters who seek donations need to know what is needed and what's out of stock. The system must be very easy to use as it will be managed by volunteers who come and go as they are available. Web-based would be ideal so that it's easy for others in the organization to access. And of course we are a non-profit so there's no money for this. An upfront cost (or possibly annual - that at least gives us a year to try it out) could be a possibility.
OpenBravo can do inventory management, among others. It is designed for companies but will cover your use case too. OpenBravo is accessed via its web interface.
Free and open source.
For the sake of closure... the organization where I volunteered ultimately chose to use Quickbooks, which has an inventory management component.
We were able to create SKUs, populate an inventory, and then periodically publish a "catalog" for others within the organization to view inventory. We set up the software on a laptop in the warehouse, and trained a few folks on how to use it for checking items in and out. Periodically we would "true up" the inventory -- typically when an item was nearly out, or if we got a large donation.
If you want to get fancy, you could set up barcodes for each SKU and use a scanner to stock or deplete them. We never found this to be necessary, but Quickbooks has the feature.
For a non-profit, you can purchase discounted versions of Quickbooks (either the software or on-line versions) from TechSoup.org.