There are two components to consider when discussing the use of web technology for human resources (HR) applications. The first component is the administration side of HR. These consist of the actions that HR personnel take to monitor and manipulate HR data. The second consideration is that of self-service; allowing employees access to data via the web to review things like sick time used, next anniversary date, remaining vacation time in the year, etc.
Small business HR departments tend not to use web-based applications for the housing and administration of employee data for two main reasons. First, there is a huge concern with the theft and sensitivity of personal information (e.g. social security numbers, birth dates, etc.). Second, HR personnel may feel it is a loss of control of the data. If HR files are typically kelp in a locked cabinet they are only accessible to those with the key. On the other hand, moving to a centralized, digital format almost always requires the need for the IT personnel to get involved. Obviously, the IT/IS personnel can access anything and everything, especially if they developed/maintain the system upon which the data resides.
The self-service portion of the system is dependent on the rest. In other words, if the data is not stored in a centralized DB, then it is not likely to be provided to employees in a web format. Organizations will continue to adopt the web-based application model for HR as people become more familiar/comfortable with putting important data online, and knowing it can be secure.
I have built extensive business information systems (BIS) that include an HR component. The HR director can manage data and everyone can view their current info. Such systems provide login-based, self-service that streamlines operations by saving time, and providing information in an always-available manner.