There's a Package for You
Idea suggested by Coniuratio.
This is another idea that's especially suited for those in long-distance relationships. Many in such situations have resorted to the classic surprise of sending a package with a little gift. Great idea, but it's not what we're suggesting.
Coniuratio's idea is to tell the person you want to surprise that you've sent them a package and that the delivery service said it would arrive at a certain time. That person will be eagerly waiting for whatever might arrive at that time. What they won't expect at all is for you to show up instead of the delivery person. If you also show up carrying a package with a little gift inside... you'll have nailed it :)
Of course, before taking action, it's wise to ensure that the person you're surprising has a relatively free day or is occupied with "fake" commitments. To gather this information and to falsely occupy their day, you'll need an accomplice from their circle.
One last tip: if the idea is to spend the day with the person you're surprising, you can put the cherry on top of your big surprise by planning the day carefully to make it unforgettable: book a table for a nice meal, plan a picnic, or an afternoon at the spa...