The December 2008 edition of the Journal of Communist Studies and Transitional Politics includes an excellent article: "Putin in Russian Fiction". The article discusses depictions of Putin in a number of works of fiction, either occupying centre stage, performing a secondary role, or making a cameo appearance. I again strongly encourage reading the whole article, but here are some highlights:
In the 2001 novel Gospodin Geksogen, Aleksandr Prokhanov constructs a portrayal of Putin precisely around elusiveness as his dominant trait.
Prezident (2002) portrays Putin as a man of flesh and blood, whose decisive actions bring a resolution to the armed conflict in Chechnya.
And my favorite:
In Russia...there has been a long tradition of suffusing the genre of fairy tales...with political satire, to voice the author's critical opinion of certain aspects of the regime in an accessible form and to try, at the same time, not to get into trouble with the censors...
An early example of the fairy tale genre targeting Vladimir Putin is Natal'ya Babasyan's 'Gadkii Putënok' ('putenok' is an amalgamation of Putin's surname and the Russian word utënok, 'duckling'; it can approximately be translated as 'The Ugly Put-ling'). 'Gadkii Putënok' was published on 6 January 2000, almost immediately after Yeltsin's resignation upon which Putin had become acting president.
A cross between Hans Christian Andersen's 'Ugly Duckling' and George Orwell's Animal Farm, it tells the story of an unattractive but assiduous duckling (Putin) from a poultry yard, who is noted for his diligence and reliability by the Mole (presumably an allusion to the tycoon Boris Berezovskii, who is widely believed to have helped Putin to take over the Kremlin) and the Ginger Cat (modelled, it seems, on the politician Anatolii Chubais, who may have recommended Putin for his first job in the presidential administration30).
With their assistance, the duckling is taken to the household of the Old Farmer (Yeltsin) to manage the poultry yard on his behalf. The duckling's unfortunate appearance plays an important part in his promotion because the Old Farmer's protg is not supposed to be loved by the domestic fowls more than the Old Farmer himself.