Answers

First, clean out the existing caulk the best you can with a utility knife, flat razor or a putty knife.  To get it extra clean and depending on what type of caulk was there before, you can use baking soda and a rag to remove hard water build up and caulk residue.  Once you've done that, I recommend GE Silicone 2 or Dap Kitchen and bath caulk.  (I like the small hand tubes, not the kind that goes in a gun.)  Water based caulks are easier to work with, but silicone has it's advantages.  To apply silicone, clean and dry the area, apply a small bead, then spray the area with soapy water.  This will keep the silicone from spreading up the edge of the splash or onto the counter.  Then wipe once with your finger and your done.  The waterbased caulk can be applied in a small bead and then cleaned up/smoothed with a wet rag.