Go for My Leave Logger, here is what they say about their software:
My Leave Logger is the ultimate absence tracking platform. Allowing users to book, approve and manage holidays, log sick days and login from mobile and desktop devices 24/7, My Leave Logger simplifies staff management and allows unlimited access to absence bookings and records, when you need it.
If you are setting up a spreadsheet then you could perhaps make use of the Bradford Factor as one of the ways you can analyse absence. You could input a formula onto your spreadsheet to calculate each person's Bradford Factor Score.
The Bradford Factor looks at the number of occasions of absence and the number of days of absence but places emphasis on the number of occasions of absence owing to the impact that intermittent absences have upon a business (i.e. staff phoning in sick at the last minute for one / two days absence as opposed to someone off long term sick who you know in advance is not going to be in at work for a specified number of weeks).
The Bradford Factor uses the formula:
Number of Occasions Sick (S) x Number of Occasions Sick (S) x Total Number of Days Absent (D) - this formula would give each person a score
You would never use the Bradford Factor in isolation when looking at absence as you always have to be aware of underlying medical conditions, if someone is not off because they are personally sick but because of family/domestic issues etc but it can be a useful tool.
The above information is just a short intro to the Bradford Factor. Let me know if you want me to post some more info on it.