Redundant weapons. In most games, this applies to pistols of any variation except for emergencies, and in many modern games, you can just replace your pistol (Secondary Weapon) with another Machinegun or Shotgun.
As an example, any pistol in the Call of Duty series. I would rather have a rifle and a shotgun for any situation than only one of those and a shitty pistol for emergencies. The pistols are weak, frequently imprecise, and have a lack of ammo available. They serve -no- purpose other than to give you a weapon at the start of the level to replace ASAP.
Other examples of redudant pistols are the Doom 3/Half-Life variety. You know, you start out with this shitty-ass weapon and work your way upward? It feels a little disappointing to me that your initial weapons just lose all their significance (In Doom 3 I just stopped using all other weapons once I got my hands on the Plasma Rifle, and the same applies to the M16 in Half-Life and the SMG/AR2 combo in Half-Life 2) later on and become a waste of space and ammo drops.
Some games make pistols okay, like the original Halo, where the pistol was arguably one of the most powerful weapons available, but in a similar vein the Plasma Pistol was completley useless. I played Dead Space recently and found that the Plasma Cutter you carry as your first weapon remains useful all the way through, especially with the ability to upgrade it to suit your increasingly annoying habit of getting into fights with slavering alien monsters. Dead Space had all the weapons be a viable alternative throughout the game, which I really enjoyed.