Microsoft Customer Resource Management (CRM) software is available free through their BizSpark program, along with nearly all Microsoft products. It's pretty easy to see if you qualify as a start-up.
http://www.microsoft.com/BizSpark/ Hope this helps.
You could try Tactile CRM (http://www.tactilecrm.com/ ), which is web-based and has a free package allowing for up to 250 contacts and 20 opportunities. I use it at the moment and like it. £6/$9 per month gets you unlimited contacts and unlimited opportunities plus it integrates with other third party apps.
Another example is Oprius (http://www.oprius.com/ ) but I don't have any personal knowledge although I've heard it is good. BatchBook (http://www.batchblue.com/ ) is another that gets good reviews from users and I had a quick look around it but preferred Tactile.
Hope that helps,
Tom