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Some verbs are followed by da:
And others by di:
Is there a rule? If not, is there a list where I can get more examples of either?
The examples you reported with preposition "da" correspond to the passive voice in which the agent is always preceded by the preposition "da". You can distinguish them because you can always rewrite the sentence in the active voice an then the agent preceded by "da" becomes the subject of the sentence. Let's do it in your examples:
Sono ossessionato dalla vostra lingua --> La vostra lingua mi ossessiona.
Sono spaventato dalla morte --> La morte mi spaventa.
Il secondo pianeta era abitato da un vanitoso --> Un vanitoso abitava il secondo pianeta.
Era disprezzato da tutti --> Tutti lo disprezzavano.
You can't do that in the examples with preposition "di".
As @Charo remarks, all the examples in the first group include transitive verbs in the passive voice, where the agent (i.e., the person or thing actually performing the action: la vostra lingua, la morte...) is introduced by da.
The verbs in the second group could have an agent introduced by da too, if constructed in the passive: “I desideri del bambino vengono soddisfatti dalla mamma”, “Greta Garbo viene sognata ogni notte da tutti i suoi ammiratori”.
Vice versa, when not in the passive, the verbs in the first examples don't need da (nor any other preposition, being transitive verbs): La nostra lingua ossessiona nachocab, and so on.
As for di, finally, it is typical of certain constructions of certain verbs, such as those in the question and several other, especially about thinking, asking or relating stuff (“Penso di arrivare in tempo”, “Gli ho chiesto di portare un amico”...). Notice that some of these verbs may have other constructions too (Ho sognato uno gnomo, Gli ho chiesto che cosa volesse).
