I work at a ~60 employee company, and while we have apps they do all of the above, they're not that usable (having been designed and written about 10 years ago). The biggest issue is HR apps are not our core competency, so management seldom allocates budget to update these tools.
Our apps do the following:
- Time off
- Shipment request (i.e. UPS, Fedex, etc)
- Purchase order request (part of this process is still paper based)
- Employee directory (currently a hodgepodge of excel sheets, paper booklets and a 14 year old intranet site)
- HR news/communications (recently purchased a hosted wiki app for this, seldom used anymore)
The biggest selling point for us would be to have the app outside the firewall, and accessible from our mobile devices or home computers.
Beyond that, having the app be a "one stop shop" for HR information (benefits, corporate policies, etc), time off requests, shipment requests and an employee directory listing phone extensions, emails, photos, bio, etc. It definitely doesn't need to be everything to everyone, but if it was a place I could reliably go to for benefits information, time off, it would surely take off at my company.