How to prove the security of block ciphers I see very often proofs of security for asymmetric crypto algorithms, for instance, using reductions to known hard problems, or game based proofs...

In the field of protocols (like authentication) it happens too, for instance proofs using formal models...

But what about the symmetric crypto? More specifically, the blockciphers?

For example, this paper (presenting the Piccolo blockcipher) has a section named Security Analysis on which the authors just argue why they think Piccolo is secure against some knowns attacks. This is actually the opposite of the "philosophy" of the provable secure crypto, that tries to analyse the security of a primitive without exhaustively trying the known attacks, because it may exist some attack that is not know by the academic community.

Thus,


Are the blockciphers usually proved to be secure?
If yes, how is it done? If not, how the security is measured?
Is the approach of security analysis used in the paper above common on blockciphers papers?
And since the answer to the first question seems to be no, is there any blockcipher whose security analysis was done following a "provable secure like" approach?
There is actually a field of study regarding provably secure block ciphers.  The seminal paper was "How to construct pseudorandom permutations from pseudorandom functions" (1988) by Luby and Rackoff.  Their paper used pseudorandom round functions in a Feistel construction, and proved that 4 rounds were sufficient to make the resulting block cipher a pseudorandom permutation against chosen plaintext and ciphertext attacks.  That paper spawned a cottage industry of similar papers based around the Feistel construction, or generalizations thereof.  In addition to academic papers and theoretical cipher constructions, this also inspired a few actual concrete block ciphers, such as the BEAR and LION ciphers by Anderson and Biham that Marcellus mentioned, and the Turtle block cipher, by Matt Blaze, for which the author claims that "recovery of its internal state given its inputs and outputs in NP-complete."

More recently, a similar wave of papers have developed regarding provably secure "key alternating" block ciphers, which are like AES in that the round function consists of the entire state being xored with a key, followed by an unkeyed permutation.  The seminal paper for this wave was 
"A Construction of a Cipher From a Single Pseudorandom Permutation" (1991) by Even and Mansour, which focused on the security of a key alternating block cipher with a single round.  This was then expanded to iterated constructions with multiple rounds in "Tight Security Bounds for Key-Alternating Ciphers" (2013) by Chen and Steinberger, inspiring a similar cottage industry of related papers in recent years.

But the overwhelming majority of actual, concrete block ciphers are not provably secure in the sense of the above literature.  Instead, they accumulate confidence over time insofar as they continually resist cryptanalytical efforts.  As Biv described, they may also attempt to prove immunity to certain specific kinds of known attack; whereas the academic papers above purport to prove security against all attacks, known and unknown.