Sachin Tendulkar. He is almost a god here. For those who don't know like sharapova he plays cricket and one of the best in the history of cricket. You can even say he is the messi of cricket.
Football - Konstantin Vassiljev, Ragnar "Raku" Klavan and if we talk about the future then I think Frank Liivak will become Estonia's best player, he currently plays for Napoli youth team.
Basketball - Kristjan Kangur
Tennis - Kaia Kanepi
Discus throw - Gerd Kanter
Fencing - Nikolai Novosjolov, Julia Beljajeva, Erika Kirpu
Cross-Country Skiing: Petter Northug(Despite of his average season and the drunk driving incident), Marit Bjørgen.
Alpine Skiing: Aksel Lund Svindal
Golf: Suzann Pettersen
Biathlon: Emil Hegle Svendsen
Etc.... etc.....
Tried to think about the biggest football star in the country right now, but couldn't land on a name since they all are scrubs. Luckily it looks like the younger generation might be able to actually do well in the future. Some good talents coming up and the likes of Nordtveit and Omar doing decently-good overseas. Think Henriksen is doing well in Holland as well although I haven't followed his progress...