Harrison. Who is awesome and definitely one of my favourites (Sneasel became one of my favourites because of him).
But Paul is by far my favourite. He had (past tense since we have his green haired knock-off now) the most unique character brought into the series and had the most passionate rivalry with Ash of any other which resulted in a huge, EPIC final battle that the underdog (Ash) won.
Gary comes close since he provided a similar challenge to Ash as Paul being more talented and I like how close he has now grown to his formal rival a great conclusion to their rivalry. Richie also comes close since it was like Ash competing against himself (but with more experience/intelligence) it was a very interesting rivalry.
I hate Trip. It is like they combined Gary, Paul etc. and then took away the interesting parts.