Summarize the following:
Several cloud based web portals facilitate recording of phone conversations without the additional hassle of installing any software or purchasing hardware. The service calls both the source and destination numbers, bridges them, and records the call. The service is tightly integrated into a telephony infrastructure which resides in the cloud. This allows providers to store recordings in the cloud and make them available to subscribers through personal portals. Some of such services are www.recordator.com, www.saveyourcall.com etc and a list of such services can be found at this Wikipedia article[1] All your call recordings are made available by the providers in your personal dashboard and you can download them as well. At first, you need to create your personal profile on their website and purchase calling minutes according to their pricing plans. Average call + recording pricing varies from 10-25 cents per minute depending on which plan you choose. You need to take care of the legal angle. So if your location requires two party consent, the onus in on you to inform your caller that the call is being recorded.

Summary:
Use cloud-based web applications. Most of such services utilize the 'Cloud-Bridge' technology. There are several providers. They  can be used with any type of phone(fixed line or cellphone). All such web applications follow a subscription based model. They do not inform your caller that the call is being recorded.