Blastoise can function well in standard play as a bulky Water; although it faces competition from Milotic, Suicune, and Swampert, it has a niche in Rapid Spin. Furthermore, Blastoise is a good spinner in its own right, as it does well against Skarmory, Cloyster, and Forretress, can take anything Ninjask might throw at it, and can get rid of Celebi's Swords Dance and Suicune's Calm Mind boosts.
Blastoise looks great on paper as it is able to hold off Baton Pass users, Metagross, Suicune, Salamence, and to an extent, Tyranitar. However, it gets worn down quite quickly as it has neither Swampert's good resistances nor Milotic's reliable recovery. Therefore, it shouldn't see much use in standard unless you're going for semi-useful novelty.
Rest Blastoise should always be used with cleric support, as RestTalk Blastoise is greatly outclassed by the aforementioned bulky Waters. In general, try your best to keep Blastoise alive, and use it only times of dire need. In fact, if you can afford it, Wish support will go a long way. In terms of EVs, a little Speed will come handy against Metagross and Tyranitar, but you might also want to consider shifting them to Blastoise's defenses or Special Attack.
Hydro Pump is a more powerful alternative to Surf, but its 80% accuracy is less than ideal. Earthquake hits the aforementioned Raikou, but doesn't do much damage because Blastoise's Attack is average at best, and investing in it detracts from Blastoise's physical bulk. Hidden Power Electric 2HKOes Gyarados, while Hidden Power Grass helps against Swampert, but they won't really come in handy most of the time. Blastoise can use Substitute and Focus Punch, but this strategy is only effective against Blissey.
Mirror Coat might work against Zapdos, but will only catch Raikou if Blastoise also has Earthquake, as otherwise it'll just Substitute. Counter works well if a physical attacker tries to beat Blastoise one-on-one, but it's generally better off using Surf or Ice Beam for coverage against Rock- and Ground-types. Haze and Roar work against Baton Pass users and Reversal / Flail Pokemon to an extent. Yawn is a fun move; lay down some Spikes beforehand for better results. Toxic is always fun to toy around with; Blastoise will likely be able to poison other Water-types, and its standard Electric switch-ins aren't fond of Toxic either.
Checks and Counters
Blastoise cannot really do much to Suicune. While Blastoise can Toxic and Haze or Roar away Calm Mind boosts, Suicune's Pressure ability and repeated Calm Mind-boosted Surfs will be Blastoise's demise. Zapdos, Raikou, and Jolteon hurt Blastoise with STAB Thunderbolt, but they have a rather difficult time coming in on STAB Surf, or in Zapdos's case, a super effective Ice Beam. Blissey and Snorlax wall Blastoise to no end, as does Regice if Blastoise cannot Mirror Coat its Thunderbolt. Ludicolo isn't hurt by any of Blastoise's moves except Toxic, while Venusaur just needs to avoid Ice Beam and it will be sitting pretty. Finally, Blastoise should beware of Exploding Metagross.