I'm trying to install Open CTI Connector to Salesforce (Professional license). The installation always fails giving me this: installing this package requires the following feature and its associated permissions apex classes. Is there any solution besides purchasing API access?
Purchasing API access won't solve that problem, API and Apex are 2 different features. Your only option for professional would be to either find an appexchange solution, which would be allowed to install and execute the Apex related to the solution. Or, find a completely external cloud based solution that only integrated via the browser, and not internal to Salesforce. Last option, of course, would be to upgrade to Enterprise Edition.
I agree with JimRae on this one, purchasing API access won't solve this issue. The only option for pro would be to find an external cloud base solution that integrates only through a browser and not internally to Salesforce. Or you can look for an app exchange solution that would install and execute your apex solution. Or just upgrade to Enterprise Edition like what JimRae said.