If you have an .xlsx file you want to use in ArcGIS but do not have Excel 2007 installed, you will need to install the 2007 Office System Driver. It can be downloaded from the Microsoft Download Center. If you do not have any version of Microsoft Excel installed, you must install that driver before you can use either .xls or .xlsx files. If you have Excel 2010 installed, you must still install the driver.
http://www.microsoft.com/downloads/details.aspx?FamilyID=7554F536-8C28-4598-9B72-EF94E038C891&displaylang=en
Source: http://forums.arcgis.com/threads/6880-.XLSX-PROBLEM-Failed-to-Connect-to-Database-Class-Not-Registered
(Raycarnes)
Hope this will help. this is copied from the original author.