Known in chess as the "Magician from Riga", Tal excelled in tactical attacks. His natural instinctive talent for the game was the prime reason for annexing the World Title from Mikhail Botvinnik in 1960 at the tender age of 24 (only Kasparov has beaten that, at the age of 22). He introduced intuitive playing style into the largely scientific-based approach of other grandmasters.
His playing style scorned by ex-World Champion Vassily Smyslov as nothing more than "tricks" yet he convincingly beat every notable grandmaster with aggression and intuitive sacrifices. Tal's intuitive sacrifices created positions of incredible complications, and it was not possible to solve all the problems over the board. Even though, in later deeper analysis after the game that flaws were found in Tal's conceptions, he still amazed and wowed onlookers by his bravery and courage. He became a spectator favourite.
His dominance over Bobby Fischer in his early years made Tal's rise to the top much smoother. Botvinnik was vanquished rather quickly, but he struck back in the return match in 1961 after a lengthy study of Tal's style (Tal's ill-health greatly contributed to his defeat).
Viktor Korchnoi and Boris Spassky are probably the only two grandmasters that mastered Tal over the board, and one of few people with a sizeable plus score against him.
Tal's playing career was affected at several points by his ill-health. He was dogged repeatedly with liver problems (possibly exacerbated by smoking) and that robbed him of many achievements. Though these illnesses did not affect his positive approach to life, famously commenting on one of his wins shortly after leaving hospital as: "The dead man played well".
Tal's best achievement was an equal first with Anatoly Karpov in the 1979 Montreal "Tournament of Stars" - there he played in his typical natural style and delivered a superb performance against the best grandmasters in the world at that time.
Tal's speed of calculation was superb, on a rarefied level with Petrosian and Kasparov. Out of the current top-level players, Alexei Shirov has probably been greatly influenced or inspired by Tal's style.