Electabuzz has amazing type coverage with its spread of attacks. This, combined with its high Speed, turns it into a real offensive threat. The reason it's not used as much as Pokémon like Raikou is that it is really fragile. This means that you have to predict switches, non-damaging moves, or bring it in on a weak attacker or after one of your Pokémon is KOed.
Electabuzz is a dangerous threat because it has such a diverse special movepool with all the elemental punches and STAB Thunderbolt, and Cross Chop to take out any special walls.
Electabuzz will generally be using Thunderbolt because of its high Base Power and STAB. Ice Punch hits all Ground-types but Piloswine, Quagsire, and Steelix super effectively. Fire Punch covers Steelix and the rare Piloswine, leaving only Quagsire, who, like Piloswine, is rare. Fire Punch also nails Scizor and Forretress on their 4x weakness as an added bonus. That leaves only Grass- and Electric-types resisting Thunderbolt (all fully evolved Dragons are neutral to Thunderbolt, although Ice Punch still hits Dragonite hard). Grass-types are covered by both Fire Punch and Ice Punch. This means that only enemy Electrics (and the UU Quagsire) can resist your primary STAB attack and not be weak to one of the punches.Team Options & Additional Comments >>>
Electabuzz can use Thunder Wave to hit enemy Electric-types, but it has two problems. First, Thunder Wave + Cross Chop is an illegal combination, so you cannot hit Blissey, Snorlax, Tyranitar, and Umbreon very hard. You can solve this by using Zap Cannon instead of Fire Punch. You do not want to lose Thunderbolt here because, although you would already have Zap Cannon as an Electric attack, you'll find that its consistency of damage is far more useful than hitting Forretress, Piloswine, Scizor, and Steelix, so drop Fire Punch and keep Thunderbolt and Cross Chop. However, this still runs into the other problem of trying to counter Electric-types in this manner. You stop Jolteon and cripple enemy Electabuzz, but the most common Electric-type by far, Raikou, almost always carries Rest, meaning it will just heal itself of status. You can use this to your advantage, however, if you want to set up a Belly Drum Charizard. BellyZard has trouble sweeping if the opponent has a healthy Raikou kicking around on their team, because it's faster than Charizard and easily OHKOs it with Thunderbolt. If you can paralyze their Raikou, when you bring out Charizard later in the game, you can use Belly Drum and not have to worry about them switching to Raikou and forcing you to switch. The other popular Electric, Zapdos, is weak to Ice Punch and doesn't resist Thunderbolt, so it's not as much of an issue.
Reflect and Light Screen help both Electabuzz and the team survive. Which one you use depends on what you have problems with. Reflect helps Electabuzz take on Snorlax better, letting it actually take an Earthquake, but Light Screen helps versus those enemy Electric-types that Electabuzz always gives free switch-ins to. Electabuzz can also use Counter, as it survives most physical hits that aren't Earthquake with a little bit of HP, and Counters it back for a near guaranteed OHKO. Electabuzz still has enough Speed after doing this to be useful, unlike, say, a weakened Counter Snorlax.
Checks and Counters
Other Electric-types are Electabuzz's best counters, since they can take all three of its main attacks without much trouble. Once you have Electabuzz in, there aren't really any real counters besides said Electrics; it's just that it has a tendency to die quickly and is hard to switch in a lot of the time.