Removing counter tiles to reveal concrete base
As Isherwood suggested, elbow grease by the drum will be required.  You can likely get the tiles off with a hammer &amp; masonry chisel.  From there, you can knock off alot of the thinset (assuming that's what they used) with the masonry chisel, but to get a presentable surface will likely require you to grind the whole thing to remove the remaining thinset.  

This will be a tricky business.  If you use an aggressive tool &amp; abrasive, you risk gouges and exposing voids or aggregate in the substrate.  If you go with a milder abrasive, it will take forever.  In either case it will create alot of hazardous dust, and there's a good chance that whatever you find under there won't make a decent looking countertop anyway. 

Are you sure this is a solid concrete countertop underneath?  It's usually some kind of concrete backerboard (if you're lucky) or particle board.

If it were me and it is solid concrete underneath, I'd knock the old tile off with a chisel, grind the thinset down reasonably smooth, and set new tile on it.  Maybe some of those bullnose counter-depth granite tiles.

If it's not a solid concrete substrate, tear the whole business off - tiles and all - and start from scratch.