Here are some CRM systems that have specific offering to Nonprofit Organizations

1. Open CiviCRM
2. Microsoft Dynamics CRM
3. SalesForce.com Foundation
4. Convio

You may notice that a major vendor is missing from the list above.  Since I would not personally recommend Blackbaud Enterprise CRM, I have not included them a link to their site.

There are other open source CRM solutions that may also be good for nonprofit organizations but I have not investigated them thoroughly yet. One other open source project of note though is OpenERP.com. I have not seen any customizations or tailoring for nonprofits though.  OpenERP is much more that just a CRM, it is offers a complete enterprise solution that includes: accounting, CRM, HR, marketing, project management, warehouse management, and more.

Good luck with your CRM vendor search.

–Mike Wood