Is it possible to create a file that will contain its own checksum (MD5, SHA1, whatever)? And to upset jokers I mean checksum in plain, not function calculating it.
Sure, you could concatenate the digest of the file itself to the end of the file. To check it, you would calculate the digest of all but the last part, then compare it to the value in the last part. Of course, without some form of encryption, anyone can recalculate the digest and replace it.
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I should add that this is not so unusual. One technique is to concatenate a CRC-32 so that the CRC-32 of the whole file (including that digest) is zero. This won't work with digests based on cryptographic hashes, though.