The common method for entering GEO orbit is to launch in what is known as a Geosynchronous Transfer Orbit (GTO), which has an apogee at GEO altitude, and a perigee of a few hundred km. Effectively all GEO missions insert their payloads into a GTO (and not into a LEO parking orbit as the OP suggests). There is no benefit of stopping in LEO first, as the only difference is that the GTO orbit has a much higher velocity at rocket burnout (it is this extra velocity which is translated into gravitational potential energy at apogee).
The booster upper stage is separated from the payload at low-Earth altitudes and the satellites coasts to apogee where it uses on-board propulsion to circularize the GTO orbit into GEO, typically over the course of several orbits. Take a look at the Falcon 9 user's guide, page 27, for how a mission to GTO looks. The main reasons to use this concept of operations are to gain the benefits of staging the upper stage rocket mass
Launching straight to GEO is practically impossible — assuming that this would be defined as the rocket being responsible for separating a payload in GEO. The only feasible means of doing it would be to add an upper stage to the rocket that would accomplish the same function that the satellite propulsion does for GTO-to-GEO circularization. But since the sequence of events in the same this is a distinction without a difference where you've just renamed the satellite propulsion system as a part of the rocket. GEO orbits are at ~42,000 km, where as high LEO is ~1,000 km. You simply have to coast your way to GTO as it takes hours to get there (using anything remotely like currently available rocket technologies).
It is worth mentioning that technically most rockets do enter LEO for some point in time, although they typically don't stay there for very long. I believe most Falcon 9 missions to GTO are in a very low "LEO" orbit for on the order of 20 minutes between first stage burns, for instance.