Parallel isn't inherently slower, but it does introduce challenges what serial communication does not.
But many of the fastest links are still parallel: The front-side bus in your computer is typically highly-parallel, and is usually among the fastest interlinks in a computer. Fiber optic connections can also be highly-parallel by carrying multiple wavelengths over a single fiber. This is expensive and therefore not typical, though. The most common form of Gigabit ethernet is actually 4 parallel channels of 250Mbit Ethernet in a single wire.
The most pronounced challenge introduced by parallelism is "crosstalk": when signal current starts or stops, it momentarily induces a small current on the wires next to it. The faster the signal, the more often this happens, and the more difficult it gets to filter out. Parallel IDE attempted to minimize this problem by doubling the amount of wires in the ribbon cable, and connecting every other wire to ground. But that solution only gets you so far. Long cables, folds and loops, and proximity to other ribbon cables all make this an unreliable solution for very high-speed signals.
But if you go with only one signal line, well then you're free to switch it as fast as your hardware will allow. It also solves subtle synchronization issues with some signals travelling faster than others.
Two wires is always theoretically twice as fast as one, but each signal line you add subtly complicates the physics, which may be better to avoid.