This question bugged me for a long time now, so I might just as well ask.

In Jim Breen's great free dictionary many verbs are marked as "transitive" (他動詞) or "intransitive" (自動詞). As far as I know these two mean whether a verb usually has a direct object or not. "Transitive" requires an object while "intransitive" does not require one.
I'm (still) not a native English speaker, so maybe I just don't understand this well.

For example: The first meaning of 触れる (fureru) is "to touch, to feel" and it is intransitive. One example sentence given to this in the Tanaka corpus is: ガラスに手をふれるな。 (Don't touch the grass.)
Why is there an object (手) in that sentence?

I have my theories about this but asking them would be too complicated.

I hope someone can help. よろしくおねがいします。

disclaimer: Yes, I know that the corpus can have errors and many translations are changed to fit the English language, but I have seen objects written for "intransitive" verbs many times before.

Notice that in all of the examples in the Tanaka corpus, the word which is the direct object of "to feel" in English is not followed by を in the Japanese sentence; they all seem to be followed by に, except when they are the topic of the sentence. So "fureru" may be marked intransitive in EDICT simply to warn an English speaking user that the English direct object will not be a direct object in Japanese.

Other examples of verbs which are similarly marked intransitive are iru (to need) and wakaru. In both of these cases, the word that is the object of the verb in an English sentence is usually marked by が instead of を, making it the grammatical subject of the Japanese verb. (Again, it can occasionally be the topic of the sentence instead.)

What are some other examples where verbs marked intransitive have objects marked by を? My guess is that in each case, the word marked by を is not the word which is considered the direct object of the verb in the English translation.

Does this mean that the grammar markings were created with the English language in mind? I don't think that is the case. For example the verb 分かる is intransitive, as it means "to be understood" and not "to understand". No sentence has any object for 分かる in the corpus.
But it might be likely that the object for some intransitive verbs were not direct objects. Maybe I should study some English grammar before I start studying Japanese.

At the moment I don't remember other examples for objects with intransitive verbs, but I'll write those down the next time I see one.

EDICT was originally a Japanese-to-English dictionary, and it uses English grammatical terms. So yes, of course the grammatical markings, as well as the translations, were made with English "in mind."

I, too, have been under the impression that a "direct object" is anything which gets marked with the particle を, and that "transitive verb" means a verb which admits an object so marked. But I don't even really know that Japanese linguists agree that there is such a thing as a "direct object" in Japanese; I do know that some (but not all) Japanese linguists deny that it ever makes sense to talk about the subject of a verb in Japanese, whether or not it is marked by が. So I think any cross-language grammatical analyses have to be taken with several grains of salt; they are useful as far as they go, but cannot be regarded as "facts."

The example you gave, ガラスに手をふれるな, is quite surprising to me, which is why I asked for other similar examples. This merely confirms my opinion that verb/particle combinations ultimately have to be learned on a verb by verb basis, as verb/preposition combinations have to be learned in European languages, including English. Explanations of "what a particle means" or generalities about how they are used can only be rough approximations.