"I trust you like I trust no one"
This one means I don't trust you. You should add the "else", as Nanren noted, to mean you trust that person more than anyone you have ever trusted. Technically, the trust doesn't have to be greater than other people, but I think a native speaker would understand the implication.
"I trust you as much as I trust no one"
Even if you add the "else" to this sentence, I don't think it would make sense.