This is only going to be a partial answer, but I noticed that the previous version of this question didn't get any answers. German grammars seem to define "modal" verbs as the verbs which fall on a canonical list: dürfen, können, mögen, müssen, sollen and wollen. Coincidentally, these are six of the seven preterite-present verbs, the remaining one being wissen. But there are several other verbs which, like a modal verb, require the infinitive of another verb as an "object". (The technical term for this is apparently Catenative verb.) There are several verbs of perception like this: sehen, hören, etc. For example: Ich sehe dich rennen. As you mentioned, lassen is another one: Ich lasse dich laufen. These are not exactly the same as modal verbs though, since they require an additional accusative object not required by the second verb. So with müssen, the basic sentence plan with an intransitive verb is subject+müssen+verb, but the basic sentence plan with lassen is subject+lassen+accusative object+verb. These verbs seem to be exceptions though since it seems more typical to use the zu infinitive rather than the bare infinitive: Ich bitte dich zu laufen.
I did mention this is only a partial answer and I don't have a list of such exceptions. One of them is helfen, as you mentioned. In that case the zu seems to be optional depending on the circumstances; I'm not totally clear on the details myself. But I don't think there are any general rules and it appears that usage varies for individual verbs. Another example is Wir gehen spazieren.
Apologies for answering in English; a long discussion in German would be a bit much for me.
PS. It's apparent from some of the comments that I was unclear on something. I didn't mean to say that only verbs that take an accusative object can be exceptions. I just meant that lassen and the perception verbs do, which is perhaps a reason for not considering them "true" modal verbs. As Tilman Schmidt pointed out, helfen actually takes a dative object. Also spazieren gehen (no space prior to 1996) is considered a single verb, so not a good example. But gehen does seem to combine with a number of other verbs in a very "modal" manner, so to me it's still an edge case.
Wiktionary has a list of English catenative verbs. It would be nice to have something similar for German verbs, but I haven't been able to find it if such a thing exists. (The link in David Vogt's comment above seems like a good start though.) Both English and German make a distinction between the to/zu infinitive and the bare infinitive. English sometimes also uses a gerund where German would use the infinitive, which complicates things on the English side. According to the list, there are four verbs, other than modal verbs, which take a bare infinitive: "dare" (especially in the negative), "help" (the "to" is optional), and "come/go" (to me these are questionable). Since German and English are related, if distantly, I imagine the list for German is similar with allowances for the gerund.
