: How many types of modulation are there? I know a few types of modulation off the top of my head like common chord modulation and and chromatic modulation, but I was wondering how many different types of modulation are there

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There are 9 types:

Diatonic Common Chord
Altered Common Chord
Enharmonic Modulation using Mm7 Chord
Deceptive Cadence
Enharmonic Modulation using °7 Chord
Diminished7 -> Major-minor7
Chromatic Mediant
Common Tone Modulation
Direct Modulation

Source: Modulation Types for Musical Analysis, by Charles Francis Leinberger, Ph.D.

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My answer is there are inifinte types. The "types" that we currently accept as "types" now may change, as music changes. Indeed, if you asked the people writing Gregorian Chant for an exhaustive list of the types of modulation, I'm guessing the list would be much shorter than if you asked, say, Franz Liszt.
Here's another type:
Rhythmic Modulation according to Gavin Harrison, from his book Rhythmic Illusions:

Just as you would 'Modulate' from one 'key' to another, if you were playing the piano for instance, 'Rhythmic Modulation' sounds like you've stepped up into a new tempo. So Modulation is like taking a rhythm that is in a different tempo and superimposing it over the tempo you are currently playing in.
It may appear to sound like a tempo change but it is in fact just a different way of grouping the subdivisions...

There are also other types, even in western music, that are not so formally defined, such as instrumental and timbral modulation.
Also considering that other cultures have completely different approaches to music, you can see that the different ways music can modulate, or change, is quite a large space.

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This is just an expansion of BlakeTM's answer, included because StackExchange communities typically discourage answering a question (or in this case, a comment) by referring to a link and nothing more. Links sometimes die and we hope for the answers here to live on. That being said, Leinberger lists the following types of modulation:

Diatonic Common Chord: "The common chord is usually just before the new dominant. It has a diatonic function in both the old key and the new key."

Deceptive Cadence: "The dominant in the old key goes to vi or bVI in a major key, or VI in a minor key, which becomes the new tonic."

Enharmonic Modulation using Diminished 7th: 'The dim7 chord is respelled enharmonically so that it has logical function, either diatonic or chromatic, in both the old key and the new key.'

Chromatic Common Chord: "The common chord is usually just before the new dominant. It has a chromatic function in the old key or the new key or both."

Enharmonic Modulation using Mm7th: 'The minor 7th of a Mm7th chord is respelled enharmonically to become an augmented 6th. This chord functions as a German or Italian 6th in one key (either the old key or new key) and a IV7, V7, bVII7, or secondary dominant in the other key.'

Diminished 7th - Mm7th: 'Lowering any chord member of a dim7 chord by a semitone results in a Mm7 chord. Some enharmonic spelling may be necessary. This is usually the dominant in the new key. The dim7 is often functional in both keys.'

Chromatic Mediant: "A functional chord in the old key moves by chromatic mediant to a functional chord in the new key. A common chord is not necessary, but one may be present.

Common Tone Modulation: "One note is sustained. It is a member of a chord that is functional in the old key and becomes a member of a chord that is functional in the new key. A chromatic mediant often exists between these two chords. A common chord is not necessary, but one may be present."

Direct Modulation: "There is no possible common chord. There is no chromatic mediant between the last functional chord in the old key and the first functional chord in the new key. There is no common tone."

Note that these are from a copyrighted document and the page BlakeTM linked.