When one considers Tangrowth for use in standard play, what usually springs to mind is that it is thoroughly overshadowed as a bulky Grass-type by Celebi, and to a lesser extent Shaymin. The former has access to reliable recovery and a Fighting-type resistance, and the latter is a more potent special attacker. Both also have higher Special Defense and Speed, as well as a fantastic ability in the form of Natural Cure.
However, Tangrowth does have some advantages over his legendary rivals. Although his Special Defense is subpar compared to the other two, he boasts a much higher Defense stat. This, together with his high HP, means that he is physically bulkier than Skarmory and Forretress. He also has a higher Special Attack stat and a decent special movepool. While his Attack stat is the same as his rivals, he has access to high-powered physical moves like Power Whip and Earthquake that the others only wish they had. To round things off, he doesn't have Celebi's Pursuit weakness, so he fares much better against Tyranitar. Tangrowth certainly pulls his weight in the standard metagame, provided that you play him to his strengths.
Tangrowth is a decent physical wall and supporter who brings a good deal of advantages to the table. Tangrowth can take on powerful physical attackers such as Tyranitar and Gyarados with his immense Defense stat, and act as a buffer against other physical threats. Tangrowth has some excellent weapons in his arsenal that his legendary rivals Celebi and Shaymin do not, and the bulk of this set is built around these. Sleep Powder incapacitates one Pokemon on your opponent's team, and can be followed up by Stun Spore or Knock Off on the switch-in, allowing Tangrowth to neuter two threats to your team in two turns. Power Whip and Earthquake form Tangrowth's best offensive combination, but he can also go special if you like, though bear in mind that Celebi and Shaymin are both more reliable as special attackers than Tangrowth.Team Options & Additional Comments >>>
As mentioned previously, Tangrowth has a vast support movepool itching to be used. Tangrowth can run a Substitute + Leech Seed set, which can be effective as Tangrowth can create 101 HP Substitutes, meaning they cannot be broken by Seismic Toss. Tangrowth can also run Sleep Powder on such a set. However, Shaymin can perform the same trick with better Speed, Special Defense and the same 404 HP stat. Tangrowth can also use Reflect (but not Light Screen) for more support.
Tangrowth has a number of options for recovery as well. Synthesis can be used, but this is not viable with the prevalence of Tyranitar in OU coupled with the low PP. Rest + Sleep Talk gives Tangrowth semi-reliable recovery, but uses up half of his available moveslots and leaves him almost a sitting duck for two turns. Lastly, Tangrowth has an interesting option in the form of Pain Split, which divides the HP of Tangrowth and his opponent and shares them equally. Although this may allow Tangrowth to stay alive longer, Tangrowth has such a titanic HP stat that more often than not he will not gain all that much HP for himself, and in some cases may even lose HP to the opponent. Tangrowth also possesses a number of setup moves such as Swords Dance and Sunny Day, which work in tandem with Chlorophyll to turn Tangrowth into a strong sweeper that is a staple on Sunny Day teams. Aside from that, however, Tangrowth isn't doing much sweeping in OU.
Tangrowth has a massive special movepool that can be called upon at times. Leaf Storm is an extremely powerful STAB attack that can maul almost everything it comes into contact with, but constitutes a free switch for Scizor or Dragonite, as Tangrowth is helpless after using it once. As for other STAB attacks, Energy Ball is more reliable than Grass Knot for consistent damage, but in general the latter deals more damage on average because of how heavy most OU Pokemon are. Giga Drain is also an option to recover a little health after each use, but the low power and low PP mean it is not ideal. Lastly, SolarBeam can be used on Sunny Day teams, but turns him into bait for Tyranitar. Focus Blast is a very powerful yet very unreliable attack that does a great deal of damage to Tyranitar and Heatran. For other physical attacks that Tangrowth can use, Seed Bomb is, like Energy Ball, a more reliable but much less powerful alternative to his primary Grass STAB, while Rock Slide does a good deal of damage to most Flying-types. Finally, Aerial Ace can take out Breloom, but doesn't do much aside from that.
Checks and Counters
Despite the fact that Tangrowth has five weaknesses, countering him can be difficult because of his wide range of support moves. If Heatran switches in as Tangrowth uses Stun Spore, he will be murdered on the next turn by Earthquake. There are also very few Pokemon who want to switch into Sleep Powder. In general, you will want fast special attackers who can destroy him by exploiting his weak Special Defense, as even strong neutral or resisted attacks will sting him.
Dragonite is a great check to Tangrowth—he can switch in easily thanks to good defensive stats, a quad Grass-type resistance, and an immunity to Earthquake, only fearing status moves such as Sleep Powder and Stun Spore as well as the rare Hidden Power Ice. He can then set up Dragon Dance or wipe out Tangrowth with Fire Blast or Draco Meteor. Scizor is another potent threat, boasting the same quad Grass-type resistance as Dragonite. STAB U-turn makes Tangrowth cry and, if Tangrowth switches out, Scizor can scout the switch-in and keep momentum going for his user. Like with Dragonite, Tangrowth's only hope of winning is to catch him on the switch with status or a niche Hidden Power (in this case, Fire). Heatran is another Pokemon with a quad Grass-type resistance, but he also has a quad weakness to Earthquake, so if he walks into the wrong move he can still lose. Another common Pokemon with a 4x resistance to Grass and immunity to Earthquake is Skarmory, who can take any move save Hidden Power Fire and Sleep Powder, Roost off the damage, and attack back with Brave Bird or simply use Tangrowth as an opportunity to set up Spikes.
Other Pokemon with super effective STAB moves or useful resistances, such as Gengar, Infernape, Heracross, and Roserade should all perform excellently as well. Remember that Tangrowth's offense isn't really all that great, so if someone can take hits and attack back, there is very little Tangrowth can do to stop them, especially if Sleep Clause has been activated.