For basic recording of appointments, it is likely that you will find that iOS's built in calendar tool is sufficient to your requirements. But if you are even slightly more demanding, then you are going to have to look elsewhere. Fast Calendar & Tasks, also known as Calvetica, is an app that prides itself on not only the speed with which new tasks and appointments can be created, but also the amount of data that can be stored and displayed.
The app can be used to manage both tasks and events, and cloud syncing means that the data you add can be easily accessed on other devices and computers. Creating appointments and tasks is incredibly quick and simple, and an innovative integrated timer makes it possible to create short term reminders in a flash.
On the iPhone smaller screen, Calvetica feels a little cramped, and the month view calendar is particularly difficult to interpret. If there is anything that can be said against Calvetica, it is that it is almost too complicated, but even this has two sides. On the one hand you are afforded unprecedented levels of control over the events you create, including a great repeating task option.
As with other calendaring apps, Calvetica enables you to store a wealth of information about individual events including notes and locations as well as giving you the option of inviting others to join you at events. With a range of customisable alerts, and a fabulous iPad interface, this is a serious tool for anyone who is serious about getting organised.