Simple proof of work example?
Bitcoin ASIC miners are specialized hardware, which is capable of computing SHA-256 only. If you change almost any parameter in the Bitcoin proof-of-work, the existing miners will be useless. For instance, you could just change SHA-256 to SHA-1 or SHA-3.

To be more efficient against spammers equipped with GPU, you might want to employ a hash function that requires a certain amount of memory to compute hash. Scrypt is a reasonable choice with hundreds MBytes of RAM as a parameter, and the ongoing Password Hashing Competition will likely to produce better and faster candidates.