The reason that we typically run just in series is because of the potential problems that parallel wiring can cause.

First off though, you must understand a few things. All parallel strings must be the same size, and ideally, the LED forward voltage must be matched to provide consistant results. Also, when wiring in parallel, the current is divided equaly between each parallel string. That means that on a 700mA driver, two parallel strings would see 350mA each.

Now, the reason why parallel strings are not commonly used is because of the potential damage done when something fails. In a series string, if an LED fails, one of two things will happen. If the LED shorts, the remainder of the string stays lit, and keeps on going. If the LED fails open, the entire string goes down, but no other damage occurs.

When you wire in parallel, a number of things can happen when an LED fails, some of them being more damaging than others. If for example, you had two parallel strings on a 2000mA driver (each string running at 1000mA) and a single LED fails open on one string, that entire string now shuts down, and the remaining string now sees the entire 2000mA from the driver, most likely killing the LEDs in a short amount of time.

If an LED in the same setup were to fail closed (a short), the string that LED was in is now running at a lower total forward voltage, forcing the current per LED in in that string higher (remember, current and voltage are tied together, so when one increases, so does the other), and creating stress on all the LEDs in that string, creating more potential failures.

If the total forward voltage of each string is different, then you can also get changes in brightness between the LEDs connected to the same driver.

IMO, it's not worth the headaches, even though it could save some cash in setup costs.