Can there be intransitive verbs which take an indirect object? In the sentence "It pleases me" is "me" an indirect or direct object? What languages frequently have indirect objects in a sentence without direct objects?
Serbian has something like that, if I am understanding you right. Some Serbian intransitive sentences can still have dative, genitive and/or locative arguments; an example for this would be
она му[D] прича (о кући)[L] (she is telling him about the house) where there's both a dative listener
му (to him) and a locative topic
о кући (about the house).
We are certain that neither of these is a direct object because 1) neither is in either the genitive or the accusative (Serbian DOs must be in either one of those cases) and 2) neither can be made into the subject of a passive verb form: sentences such as
*он је причан о кући (he is told about the house) and
*кућа је причана њему (the house is told to him) do not work and sound quite ungrammatical. The only passive sentences these two arguments could fit in would be in the spirit of
причано му[D] је (о кући)[L] (it was talked to him about the house) and those kinds of sentences still retain both the locative and dative arguments.
Furthermore, it is possible to add an accusative into the example sentence, thus for example giving:
она му[D] прича причу[A] (о кући)[L]. Such a sentence can easily be turned into a passive one, giving f.e.
причана му[D] је прича[N] (о кући)[L] where the former accusative argument "причу" becomes a nominative argument "прича" in accordance with general passivisation patterns in nominative languages.
The only way these sentences could be analysed as including a direct object would be to analyse them as having a dropped or implied accusative argument, which is otherwise unheard of in Serbian.
This also has a parallel in sentences with a non-nominative subject; a sentence with a genitive, accusative or dative subject is usually intransitive, but can also have additional arguments that do not serve as direct objects.
With a genitive subject, these are most often sentences in the mould of
нема нам[D] посла[G] (there's no job for us) or have an experiencer (such as
тебе[G] ме[G] је срамота it's you who I'm ashamed of; this sentence has two genitive arguments). With a dative subject, they are usually those with experiencers, such as
хладно му[D] је (he feels cold, more directly it's cold to him). With an accusative subject, they also usually are with experiencers, such as
жао ми[A] је детета[G] (I feel sorry for the child).
Such sentences with non-nominative subjects and additional arguments but without a DO still cannot be passivised. They'd give sentences like
*посао нам нема,
*срамотан сам тебе and
*жао сам те; these sound utterly wrong and ungrammatical. The closest equivalents would have to use different verbs or phrasings for that, giving
немамо посла (we don't have a job),
тебе се срамотим (it's you who I'm ashamed of), and
жалим дете (I pity the child), which are all sentences with DOs and a dropped pronominal subject.
Under the traditional interpretation of the terms 'transitive' (= capable of taking a 'direct object') and 'intransitive' (= not allowing a 'direct object'), the answer is 'Yes'. Spanish is a case in point. In Spanish sentences parallel to It pleases me, such as (1) or (2)
El discurso del Rector ME/NOS/TE/OS/LE/LES gustó.
ME/NOS/TE/OS/LE/LES gustó el discurso del Rector.
the clitic pronominals are in the dative case and, in Spanish, where, contrary to Modern English, the dative/accusative contrast remains relevant, must be analysed as indirect objects (and, of course, cannot be converted into subjects of passive sentences, etc.). This fact does not show when the clitics are first or second person, as in that case the Spanish dative and accusative forms are, as in English, also homonymous and indistinguishable (i.e., me/nos, te/os), but it does show very clearly when the clitics are third person: LE/LES gustó el discurso del Rector (with dative clitics > indirect objects) are fine, but LO/LA/LOS/LAS gustó el discurso del Rector (with accusative clitics > direct objects) are terrible.
Yes, of course. In German, for example, the verb "helfen" (to help) is intransitive: "ich habe ihm geholfen" (I helped him). It takes an indirect object (dative) that can't be passivized.
Turkish has many verbs with so-called noncanonical (indirect) objects where one would expect a direct object. In general, just get a valency lexicon of any language and look for frames of intransitive verbs, you'll find many slots for indirect objects.