Okay so. I know you can see the last spell someone cast (from memory, this was in the Goblet of Fire), but is there a spell that can, for lack of a better phrase, clear your wands' history?
There are no "Clear browser" spells shown in the Potter books, films or other literature. You do have some other options though, if you're worried about something finding out what you've been up to.
Security by buffer overflow.
We know from Goblet of Fire that it's possible to get a wand to regurgitate the wand's spells in reverse chronological order. What we don't see is the wand continue to regurgitate spells past a certain point.
By casting innoccuous spells (such as 'lumos') several dozen times, you may push the spell/s you wish to hide beyond the wand's ability to "remember" them. This obviously assumes that the wand doesn't just regurgitate all of them regardless of age.
Security by labour-intensivity
The spells seem to "erupt" from the wand at a rate of around one every 10-20 seconds, far slower than you can cast them. By casting thousands of quick spells over the course of several days, you could hide the spell you want to hide in a mass of other spells or simply make the process too labour-intensive for your opponent to bother with. After they've sat through a few hours of lumos, lumos, lumos, lumos, lumos they've probably given up, assuming you've found a way to stop the spell from working correctly.
Security through lack of interest
Priori Incantato seems a pretty rare and powerful spell and Priori Incantatem doubly so. If you avoid doing anything exciting with your life, it's unlikely you'll ever be put into a position where one of these rare powerful witches or wizards takes sufficient interest in you to actually cast this spell.
Security by "snap"
Broken wands can't be repaired except through the application of the most powerful magic. Snapping your wand in half would seem an excellent way of preventing the memory from being read, especially if you have a small supply of spare wands lying around.