The list isn't meant to be exhaustive or carefully arranged. Any additions, corrections or further examples would be welcomed.
1 main verbs; lexical verbs (all verbs which are not
auxiliaries or modals)
2 action verbs; event verbs; dynamic verbs (a verb which can
be used in continuous tenses) i.e. eat, run, talk
3 state of being verbs; existence verbs; state verbs;
stative verbs; static verbs (a verb which describes a state and is not usually
used in a continuous tense) i.e. be, own, know
4 regular verbs (a verb that has four forms and follows the
normal rules)
5 irregular verbs; strong verbs (a verb not following the
normal rules for inflection)
6 auxiliary and modal verbs (which make up verbal phrases) –
23 in total
7 linking verbs; copulative verbs; copulas (a verb which
links the subject and complement of a clause) i.e. It is warm today.
8 transitive verbs (a verb used to talk about an action or
event that involves more than one person or thing, and so is followed by an
object) i.e. She’s wasting her money.
9 intransitive verbs (a verb used to talk about an action or
event that only involved the subject and so has no object) i.e. She arrived.
10 multiword verbs
a type 1 – intransitive [phrasal
verbs; adverb particle
b type 2 – transitive (inseparable)
[prepositional verbs; preposition particles]
c type 3 – transitive (separable) [phrasal
verbs; adverb particle]
d type 4 – transitive (with two
inseparable particles) [phrasal-prepositional verbs; first particle is
an adverb, second particle is a preposition]
11 compound verbs
12 delexical verbs (a verb which has very little meaning in
itself but is used with an object to describe an action) i.e. She gave a small
cry.
13 ditransitive verbs (a verb which can have both a direct
and indirect object) i.e. She gave me a kiss.
14 ergative verbs (a verb which can be used transitively to
focus on the performer of the action, or intransitively to focus on the thing
affected by the action) i.e. He boiled the water. The water boiled.
15 reporting verbs; performance verbs; performative verbs (a
verb used with a quote or a reported clause to describe what people say or
think) i.e. suggest, say, wonder
16 reciprocal verbs (a verb which describes an action
involving two people doing the same thing to each other) i.e. They met in the
street.
17 reflexive verbs (a verb which is typically used with a
reflexive pronoun) i.e. Don’t cut yourself with that knife.
18 defective verbs (a verb without all the inflected forms
of a regular verb) i.e. modals
19 finite and non-finite
a infinitives
b gerunds; verbal nouns
c participles
20 catenative verbs (a verb that takes other verb forms as
objects; found at the head of a series of linked constructions) i.e. We agreed
to try to decide to stop eating snacks.
21 causative verbs (a verb that designates the action
necessary to cause another action to happen) i.e. The devil made me do it.