Salesforce is the $3 Billion giant in the CRM (customer relationship management) software space. Long ago it was ACT! which Sage bought and still sells as Sage ACT.
Microsoft Dynamics CRM is out there for the folks partial to Microsoft.
For those partial to Google Apps, you have Insightly and Batchbook.
For folks that like a suite of services not Google or MS, Zoho has a CRM along with a host of other collab and productivity software. [Nice review of Zoho CRM at PCWorld.] Zoho has plug-ins for Outlook, Google, and QuickBooks. Zoho also has developer support.
Infusionsoft is used by many SMB, especially by internet marketing businesses.
For do it yourself-ers, there is the open source Sugar CRM, which you can host or now get hosted for you.
Highrise by 37 Signals for folks partial to Basecamp. BTW, during their 15 year anniversary, 37 Signals renamed themselves after their biggest product, Basecamp.
Landslide was acquired by J2 in 2012, which changed it to CampaignerCRM. It incorporates email marketing into the customer database.
Couple of others: Nimble and ContactMe (see reviews at CIO). Nimble is the most social of the CRMs, listening in on social networks, which makes Nimble a Social CRM app.
Pipedrive and Contractually are reviewed here (along with Highrise).
Some of these are free for single users up to 3 users. Many cost money. Some are complex; some are simple. Simple does not mean ease to use, but use you must. The reasons to use a CRM system are many, including having a database of all of your customer interactions. Customers are the reason you are in business.
In 2013, this article explains why 11 CRM apps are terrible. "These applications are terrible when managers don’t insist on the reports they should be using, don’t enforce rules for entering new opportunities and don’t commit to long-term, consistent and repetitive drip-marketing and communication campaigns using the information maintained by their CRM system to keep their prospects informed and their customers close."
This is not an exhaustive list by any means.