Not only is it possible to tile over an existing brick floor, wall or fireplace, it's relatively easy. Where most people go wrong is in adding extra steps to the process. In fact, all that a homeowner really needs to do is apply a layer of thinset directly to the brick in order to adhere the new tiles.
Not everyone likes how brick looks on an interior wall. Addressing this is often a project that many do-it-yourself homeowners put off for far longer than should be reasonable. It should be noted that the most common application of brick on the inside of a home is in and around a fireplace. With that being the case, any project addressing this should include tiles that are rated for the additional thermal stress created by the heat of a fire actually burning. These temperatures can vary depending on the type of insert, whether it is gas or wood burning, so it's important to use tiles and a grouting compound that are capable of holding up under either condition. Further, it's critical that all tiles are level on the horizontal, in order to ensure clean lines and even finishing is possible once the grout is applied.