I'm a little confused, are you asking what it is possible to do on Excel only using one worksheet? And what do you mean by application?
Unless the data you need to handle is quite large, you can pretty much get away with using Excels full functionality on one worksheet without too much hassle.
So, if you're looking for examples, you could create a personal budget spreadsheet, a time table, a scoreboard, an account balance sheet... You could even use a worksheet to calculate things like averages or percentages, or to simply keep track of data in a structured way.
