Grammatical gender often seems arbitrary from a semantic point of view. When I was taking French many years ago, we were told that one must simply memorize the gender for each noun. Are there any languages with similar markings on the verb--obligatory morphological markers for the verb that typically seem arbitrary from a semantic point of view?
Romance languages have (generally speaking) three classes of verbs, inherited from Latin. In French, these correspond to the infinitive endings -re, -er, and -ir. These are like gender in that they don't correspond to any semantic property of the verb. Unlike gender (as expressed in Romance), it's difficult to point to a single morpheme as the "gender marker." However, the different verb classes have differences that pervade the paradigm of tense and agreement marking. In the Romance context, this is sometimes called the "theme vowel," hearkening back to a stage of the language when the morphology was more segmentable.
Many other languages have a notion of "verb class" that is even less morphologically transparent. Old English for example had seven classes of strong verbs; each of these had a different ablaut pattern. (There were also three different weak verb classes.)
French and other Romance languages provide an example, actually – verbs are arbitrarily associated with theme vowels.
For example, in Spanish (I am not familiar with French), the infinitive form of to have is tener, and that of to take is tomar. The bolded vowel, traditionally called "theme", affects most of the inflected forms of the verb: tienes (you have) vs. tomas (you take), tiene vs toma (third person singular), tenéis vs. tomáis (second person plural), etc.
Crucially, these are inherent properties of the verbs, not simply a part of their phonological form: in the Spanish subjunctive, verbs with an e or i theme take a in the theme position and verbs with an a theme take e in the theme position. For example, tomas becomes tomes, and tienes becomes tengas. (Obviously, there are some other things going on here morphophonologically, but the important part is the theme vowel.)
More generally, grammatical gender, theme vowels, and the Germanic verb classes mentioned in Aaron's answer, are kinds of inflectional class (in the modern sense, not the more limited traditional sense), i.e. arbitrary groups of roots/stems identifiable by a morphological reflex.
I'll also throw in that some languages also have grammatical gender in their verbs. Polish, for example (I assume other Slavic languages do as well, but I'm only familiar with Polish).
- chciałbym = I would like (male speaking)
- chciałabym = I would like (female speaking)
- byłem = I was (male speaking)
- byłam = I was (female speaking)
English might only have one pattern of regular verb conjugation (depending on how you define "regular", the strong Germanic verbs have several sub-regularities), but many languages have several classes of regular verbs which have separate rules for conjugation. Usually these are independent from semantics.
Other than the Romance ones that others have mentioned, examples are
- Danish has two regular ways to form past tense, -ede and -te.
- Swedish has 3 regular conjugations, -er verbs, -ar verbs and -r verbs.
- Modern Japanese has two regular conjugations, godankatsuyo (5-row conjugation) and ichidankatsuyo (1-row conjugation).
The perfect example of verbal gender/verb classes would be a language that assigns every verb to one of a small number of classes and has morphology elsewhere in the sentence that agrees with the verb, e.g. declining adverbs to agree with the verb. I don't know of any slam dunk examples.
French itself, though, has an example of something similar. The selection of avoir (to have) or être (to be) for forming compound tenses is partly lexical.
A closed class of intransitive verbs use être (e.g. aller (to go), devenir (to become), naître (to be born)) and every reflexive verb uses être.
Je suis allé(e). 1sg.NOM be.1sg.PRES go.PP.M/F I went / I have gone. J' ai dormi 1sg.NOM have.1sg.PRES sleep.PP I slept / I have slept
Selection of être is highly correlated with unaccusativity, but in French the choice of auxiliary cannot be predicted perfectly from semantic criteria alone.
This paper goes into some detail about the verbs that form compound tenses with to have and to be in French and Italian.