"Mode" is a difficult word in music because it has many meanings.

The most common is probably in reference to "the Modes" - Aeolian, Locrian, Ionian, etc.

Mode also means "manner" - the way something is played (in the mode of...).

Mode also means an operation we perform on note sets, as in D E F G A B C is "the second mode of C Major" - really it's a rotation of the set.

There are also Rhythmic Modes used in ancient music!

But one meaning of mode is "version" and that is the context in which the word is used in the concept of "Mode Mixture".

Mode Mixture involves the borrowing of notes from one mode (or version) of a key and using them in another. Since you borrow them, many people also call them "borrowed notes", but most theorists prefer the term Mode Mixture when talking specifically about swapping notes between modes of a key, versus borrowing notes from "anywhere". I'll use borrow though sometimes just because it's easier to type.

Basically, a Key as two modes; Major and minor. Usually, the Major mode of a key is numbered:
1 2 3 4 5 6 7 (8 or 1).

Thus, compared to this, minor is numbered:
1 2 b3 4 5 b6 b7 (1).

Or in letter terms, in C, C Major is:
C D E F G A B (C)

and C minor is:

C D Eb F G Ab Bb (C).

Notice I'm talking about Keys here, not scales (see my article about Understanding the Minor Mode for further explanation).

If you compare Cm to CM, cm has a lowered 3rd, 6th, and 7th scale degree. In fact, all minor keys have this same relationship with a Major key with the same tonic - 3, 6 and 7 are always lowered a half step.

By the way, important fact here - since the keys we're discussing share the same tonic, we're talking about PARALLEL keys - CM and cm are parallel. AM and am are parallel. Mode Mixture occurs between parallel keys.

Mode Mixture involves using notes from the Parallel Minor in a Major key, and notes from the Parallel Major in a minor key. Since 3, 6 and 7 are the only different notes, they are the only possibilities.

In Major, use of b3, b6 and b7 are examples of Mode Mixture (caveat: tehy can be just chromatic notes, or explained in other ways too, so it needs to be clear that they're operating in such a way as the tonic is maintained, and they are hinting at the minor version of the key). Consider the following melody:

C G A G F E D-----
C G A G F----
C G A G F E D----
C D Eb D C----

The first part is obviously C major. So where does the last Eb come from? C minor - it is b3 in C minor.

Consider the following melody:
C G Ab G F Eb D----
C G Ab G F-----
C G Ab G F Eb D---
C C G F En-- C--

Again, obviously in C minor at the beginning, and then the En at the end implies C major.

Now, when we talk about the key of the piece, we'd say the first is in C Major, and the second in C minor. Each has a note borrowed from the parallel key. Because of this, it's often better to think of classical music as being "In C, in the Major Mode", or "In C, minor mode".

You may have noticed in your musical endeavors though that most music is not just melody, but harmony as well. In fact, most versions of Mode Mixture are the result of harmonic changes - sometimes referred to as "color" chords. If for example, you use fm in the key of C Major, you are "borrowing" that chord from the minor mode. Now, we can debate about whether you're just borrowing scale degree 6, or the entire chord from the minor mode, but it so happens that virtually all occurrences of Mode Mixture involve chords, not notes, that can be borrowed from the parallel key.

So let's start with Minor:

We call the altered scale degrees "raised" or "#" when we borrow them - so they are what would be the regular ones in Major. In other words, #3 in Cm is En,, since En is a raised version of Eb, and En is found in the parallel Major. Also note that # here means "raised" not specifically a sharp sign.

In minor, #3, #6 and #7 are used. Whoop, Whoop, Whoop - problem...
#6 and #7 are already used in "harmonic" and "melodic" minor. So guess what - we don't consider them Mode Mixture - we consider them "diatonic" notes in the minor key.

So really, #3 and chords containing it are the only instances of mode mixture in minor keys. And not all chords!

I is about the only common example of mode mixture in minor.
Change i (cm) to I (CM) in c minor and you have mode mixture.

There is no #iiio (E G Bb), and no VI+ (Ab C En). In other words, since we don't use those chords in Major (at least as diatonic), we CAN NOT use them as Mode Mixture either. But I does exist in Major, so it can be used in minor.

I may be used often in minor mode pieces, however, a special case must be mentioned: A very common thing to do is put a Major I chord at the end of a minor key piece (CM chord ending a piece in the key of cm). This is called a "Picardy Third" (or Picardy Cadence - and it may come within a piece as well). Apparently, it was very common in the region of Picardy and it is the third of the chord that is altered, so they named it that. Picardy Thirds are extremely common for a certain period of time (Renaissance and into the Baroque) but can be found commonly even today - the Beatles "And I Love Her" is a great example. In fact, some theorists view things like Beethoven's 9th, which is in dm, but ends in DM to be a large-scale Picardy idea. Whatever the case, that brings up the point that even if a piece ends with a Major I chord, if the majority of it is minor we still say it's in minor.


Mode Mixture in Major is more varied:
i instead of I (cm in C Major)
ii^o instead of ii (d^o)
bIII instead of iii (EbM)
iv instead of IV (fm)
v instead of V (gm)
bVI instead vi (AbM)
bVII instead of vii^o (Bb)

Note here again that the WHOLE chord is borrowed from minor, not just a portion of it. For example, iii (E G B ) becomes bIII (Eb G Bb) borrowing BOTH b3 and b7 from minor (note, classical theorists prefix a flat sign to the beginning of a Roman Numeral to show that the ROOT of the chord has been lowered a half step from its normal position).

Obviously, we don't "borrow" IV and V, and vii^o from minor because A. They're already used regularly in minor, and B. they already exist in Major!

7th chords are also possible:
i7 (cm7)
ii%7 (half-diminished 7 dm7b5)
bIIIM7 (EbM7)
iv7 (fm7)
IV7 (F7)

Here's an important one - in minor keys, there is also a IV7 - F A C Eb. You can borrow this chord in Major too, but in this case it appears that you're only borrowing one of the notes - note this chord happens in minor, so you can use this chord in Major. C E G Bb on the other hand doesn't happen as a primary chord in either Major or minor, so you can't use it as mode mixture, so I7 is impossible (in classical music, not pop styles - but even then it's not mode mixture).

v7 (gm7)
bVIIM7 (AbM7)
bVII7 (Bb7)

and last but not least, viio7 instead of vii%7.

The most common examples of Mode Mixture in Major are chords that use b6: iv, iv7, ii^o, ii%7, bVI and bVIM7 (though VI is more common in triad form) and vii^o7.

(note, iv7 and bVI use both b6 and b3)

The reason is, b6 has a strong "pull" towards scale degree 5. This has led many people think of it as an "un-leading tone" - a leading tone that pulls down rather than up. Since it pulls strongly to 5, pre-dominant function chords are often "minorized" to make them pull to V in much the same way that dominant function chords are "majorized" in minor to make them pull to i.

These progressions, like iv6-V, and ii^o-V already happen in minor and sound quite natural in Major. In fact, you can't really tell if:

fm - G - C or ii^o-V-I

is cm with a picardy third, or C major with borrowed iv/ii^o!

Next most common are those chords containing b3: i, i7, bIII, bIIIM7 (and iv7 and bVI mentioned above).

Minor i is actually fairly common, especially in early classical development sections. Since the remaining ones also contain b7 as well, they're a bit rarer, and bIII is in general a rare chord in Major (tends to sound like the Tonic of the relative major of the parallel minor!!!).

Next comes chords containing b7: v, v7, bVII and bVII7.

Minor v is more common, and bVII7 has a tendency to sound like V of the relative Major of the parallel minor, so it is used only when it's obvious it's not doing that.

Sometimes people call minor v a "modal dominant" - that sort of implies it comes from the Mixolydian mode though, and not from parallel keys.

By the way, classical theorists do not consider changing from C Major to C minor a "key change" or "modulation". We call it a "change of mode". The tonal center (C) has not changed. Many people freak out about this because they're so used to thinking about key signatures - but they call C major to A minor a key change! C Major to C minor is not a modulation, and use of mode mixture is quite common, and not only chords, but entire passages can be said to involve mode mixture. In fact, Romantic period composers delighted in trying to find new sonic resources and whereas Classical period composers may have composed a phrase in C Major, and the next phrase in C minor, Romantic period composers would fluctuate on a chord-by-chord basis sometimes - you don't know if the piece is Major or minor, just "in C".

A favorite device of Romantic period composers looking for new sounds and looking to reduce the importance of the dominant actually modified an old sound - they took plagal cadences and used mode mixture to make a "new" (to them) sound. iv-I, ii%7-I, and even vii^o7 in second inversion with the bass moving 4-1 (which is a neat combination of authentic and plagal cadence) became favorites of Schubert, Brahms, etc. Another good Beatles example is "In My Life" at the end of of the vocal sections.

So next time you're writing a chord progression, try substituting a chord from the parallel key. For example:

I - vi - IV - V

Why not change it to:
I - vi - iv - V
or
I - bVI - IV - V
or
I - vi - IV - v (a little funky)

or try two out of the four chords instead. Some will sound cool, others won't. But try out various combinations.

One last thing, just in case anyone was wondering - classical music really doesn't make too much use of 9th chords. In fact, 7th chords on anything other than V and vii^o, and to some degree ii are really kind of uncommon by comparison (that is, you can find plenty of them, but compared to V7, they're minuscule). The one common 9th chord is V9.

In Major it's V9 - G B D F A in C Major.
In minor it's Vb9 - G Bn D F Ab in C minor.
It's quite common to borrow Vb9 in Major (a more and more common device starting with Beethoven).
V9 in minor, borrowed from Major would be unlikely though.

fine.