This page will provide suggestions on what Pokemon you can consider in including to your group. Your team composition will depend on each Pokemon's moveset , type and abilities. There are a lot of good choices out there and you have the freedom to choose what you want in your team. I won't be listing legendaries because of they're already strong by default.
These make up most teams' main offensive force. Their role is to take out as many Pokemon as they can using direct attacks or lay waste after their teammates set up the stage for them. That said, we have Physical or Special Sweepers. Here are some suggestions:
Salamence's power lies in its Dragon Dance, Moxie and Outrage combination which will make it harder to be blocked by walls. Moxie allows Salamence's attack to grow even more stronger per enemy defeated. It has great base attack stat but its sp attack isn't falling behind either. It has access to a good variety of physical and special move pools making it a reliable mixed-attack sweeper.
Scizor is also one of the popular choices as a primary physical sweeper. It has a very high base stat and has multiple resistances, leaving it only with one serious weakness: Fire. Usual EV builds further boosts its attack and HP to make it bulkier. Bullet Punch is a favorite part of its moveset, along with Swords Dance. Though with a base power of 40, this priority, steel-type attack can become a deadly, STAB and SD-enhanced hitter that overcomes Scizor's slow speed. It's Technician ability further powers up this move as well.
Lucario's uncommon typing allows it to have multiple resistances against several popular types and utilize devastating STAB attacks. It is also immune to priority attacks or flinching (with the Inner Focus ability). Lucario can use ExtremeSpeed, a +2 priority move that has a base power of 80 and 100% accuracy. If boosted with one Swords Dance, its damaging potential can skyrocket to threatening levels. Close Combat is also another good move that Lucario can include in its disposal.
Gengar's high base speed, sp attack and a wide selection of special moves make it a force to be reckoned with. Shadow Ball is its main STAB move with 80 base power, 100% accuracy and 20% chance to lower the target's SP Defense. Gengar's Levitate allows it to remain unscathed when an opponent or ally uses Earthquake. Focus Blast is also a good offensive move to have in Gengar's moveset. This is further enhanced by a held Expert Belt or Life Orb. Gengar can also utilize Thunderbolt for additional coverage and Hidden Power to further enhance the versatility of its offensive arsenal.
The overused build for Alakazam focuses on speed and special attack, further augmenting its already impressive numbers on those stats. Its Magic Guard ability works perfectly with Life Orb, enabling Alakazam to dish out devastating damage without losing its HP as part of the item's effect. As a sweeper, most trainers' preferred moveset for Alakazam is all about offensive moves. Psychic or Psyshock are two of its possible STAB moves. Focus Blast allows Alakazam to deal fighting-type damage while being counted as a special. Signal Beam allows it to deal super-effective damage against fellow Psychic-types with the chance to confuse it.
Volcarona has access to Quiver Dance, one of the best stat-boosting moves in the game that allows it to simultaneously raise its Sp Attack, Defense and Speed simultaneously. Being a dual-type, it can also utilize powerful STAB moves like Bug Buzz. For a fire-type STAB move, you can consider using Fire Blast for power or Fiery Dance for a chance to increase its Sp Attack. Volcarona has an excellent base Sp Attack stat and impressive Speed and Sp Defense stats. Volcarona is very susceptible to Stealth Rock, which exploits its double weakness to rock-types. While most trainers will settle with Volcarona's default ability (Flame Body) to burn any attacker that makes contact, the hidden ability Swarm will allow it to make a last spurt by powering up Bug Buzz and punching through enemy defenses.
Hydreigon's Dark/Dragon typing alone allows it to enjoy multiple resistances, except Ice or Fairy attacks. It also has Levitate which protects it from devastating Earthquake and traps like Spikes or Toxic Spikes. Hydreigon doesn't have to worry about Stealth Rock either since its types won't cause it to lose that much HP when switching in. Draco Meteor is its primary STAB move. With 130 base power and 90% accuracy, the only downside of this move is that it lowers the user's SP attack after attacking. The workaround for this drawback is by teaching U-Turn to it, which will allow it to switch out of battle while dealing damage to an opponent and resetting its lowered stats. Hydreigon has decent speed stat but it can easily outrun by other more potent opponents. That said, trainers who use Hydreigon as a sweeper use Choice Scarf to make it act faster and do some hit-and-run attacks.
Starmie has been around since Gen 1 and its proven its worth as a sweeper and more recently, as a "spinner" (one that can remove entry hazards / traps using Rapid Spin) It has excellent speed, great Sp Attack and decent defense and sp defense ratings. It can also learn a wide variety of multi-type moves. Choice items are not recommended for Starmie since these limit it to use one move in exchange for a specific stat boost. Starmie can provide a good coverage since it can also learn Thunderbolt and Ice Beam which can be used against the commonly used teams. Starmie can be EV-trained to be a glass cannon but it can also be trained as an offensive support Pokemon. Aside from Hydro Pump and Surf, another favored STAB move is Scald. Starmie is quite frail but when switched correctly, it can effectively sweep the enemy group.
These are the Pokemon that excel in performing as walls, stallers, support etc. They play an important part in slowing down enemy sweepers and hitters while giving your team a chance to set up and go with your battle plan.
Ferrothorn is a great trap-setter and a good wall as well. It has really high defense stat with a comparable sp defense as well. Sadly its base HP doesn't live up to the defensive stats so anyone who wants it to take the tank role should EV train its HP to make it bulkier. It has access to Spikes and Stealth Rock which can deal good entry damage to those not resisting them. Aside from the remarkable defenses, Ferrothorn has the ability Iron Barbs which inflicts damage to a Pokemon making contact with it. If you equip a Rocky Helmet, the attacking enemy will lose more HP with the effect of the item and Ferrothorn's ability. Aside from being a great defensive Pokemon, Ferrothorn can still lay waste to unsuspecting opponents using its STAB moves Gyro Ball and Power Whip. The former can turn Ferrothorn's low speed to a powerful attack while the second allows it to damage multiple Pokemon at once.
Forretress is already rocking with high base defense and decent base HP. However, its speed and SP Defense are quite lacking. It also has very high susceptibility against fire attacks but it should be able to survive the hit with its Sturdy ability. Like Ferrothorn, it can lay traps and act as a physical wall. However, Forretress has access to Rapid Spin, a move that can deal a small amount of damage and remove all traps as well. Gyro Ball is its main STAB attack while trainers can either put two traps (Spikes / Toxic Spikes or Stealth Rock) in its last two slots. If Forretress is given a role to take on an offensive stance after laying its trap(s), Explosion is a good option, considering that its Attack stat is EV-trained.
Bronzong boasts excellent rating to its base defense and sp defense. It's dual typing makes it immune to two types and resistance to eight more. These alone makes it an excellent tank. Its Levitate ability also protects it from ground attacks and spike traps. Like the other slow Steel-type Pokemon, Bronzong's main STAB move is Gyro Ball. Bronzong can either be a dedicated tank or dual-screen setter. For the first role, it must hold Leftovers to gain constant HP recovery. Stealth Rock and Gyro Ball will always be part of the move set, and trainers can opt adding Hidden Power (Ice), Toxic or Earthquake. As a dual-screener, Bronzong should have Light Clay, an item that extends the duration of the screens for an additional 3 turns. Gyro Ball and Stealth Rock will be in that role's move set as well as the screens. Bronzong's lack of self-recovery moves will make it succumb to multiple attacks but that should be enough to buy you time to sweep or set up your favorite play.
Blissey's outstanding base HP and SP Defense stat makes it an excellent special wall. The downside however is its abysmal defense stat and also, being a normal type which even makes her more susceptible against Fighting Types. With proper move sets and support, Blissey will perform well as a wall and cleric. Blissey has a wide array of support moves such as Toxic, Hell Bell, Aromatherapy, Heal Pulse or even heal itself using Softboiled. Blissey can also learn Healing Wish, a sacrificial move that will fully heal the next Pokemon you'll release - perfect for a critically injured or phased sweeper. Blissey can utilize offensive moves, thanks to its decent Sp Attack. Its doesn't have an effective STAB attack (save for Hyper Beam) so Blissey may need to rely on non-STAB special moves like Flamethrower, Grass Knot, etc.
Jellicent's diverse move pool allows it to be trained as a wall, support or even offensive (but not as a main sweeper) Pokemon of the team. Its EV training will depend on the role the trainer wants it to take on. This further complements Jellicent's high HP and SP defense stats. Its other stats are already decent enough while its good dual-typing provides a wide array of resistances. It has access to a very powerful multi-target STAB move, Water Spout which damage depends on how high Jellicent's HP is. Fortunately, Jellicent has the self-recovery move, Recover. Another powerful STAB move is Shadow Ball, which deals damage and has the chance to lower the target's sp defense by one stage. Water Absorb allows it to recover some HP when hit by a Water-type move - fairly useful if you have a Surf-user in your team. Scald is its another good STAB option, with the chance to inflict burns. Unfortunately, Jellicent's "floating" animation doesn't protect it from entry hazards, ground attacks and the like.
Slowbro is highly regarded as one the most reliable Trick Room setter. With impressive base defense, sp attack and good HP and SP defense following shortly, Slowbro can become a reliable wall with self-sustainability. Its Regenerator ability allows it to heal a portion of its HP after switching out or recover its HP while remaining in battle by using Slack Off. Scald or Surf and Psychic / Psyshock are good choices for STAB attacks, thanks to its dual-typing. Like the other Pokemon in this list that can take on two or more roles in a team, trainers will need to modify Slowbro's move sets for it to perform effectively as a wall, Trick Room setter, back-up sweeper, etc.
Images and move links from PokemonDB
Additional competitive tips available at Smogon University.