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I really commonly find that contemporary songs use an arpeggiated up-and-down progression over notes that are in this shape, here are some examples:
Is there a name for this?
How can I tell which sets of these go together?
I suppose that happens in the left hand in the songs you're referring to, while the right hand plays something different?
Then it's a kind of alternate bass.
In all your examples, the pattern is first, perfect fifth, octave.
I guess you can understand why the first and the octave sound good (sound in unison), right? It's the same note.
The note in between is a perfect fifth. Wikipedia says
The perfect fifth is more consonant, or stable, than any other interval except the unison and the octave
This means that when you play a note, the 'best sounding' note in unison with it (after the octave) is the perfect fifth.
You might understand it better when you write it as 'perfect fifth' rather than 'fifth'.
The term perfect identifies the perfect fifth as belonging to the group of perfect intervals (including the unison, perfect fourth and octave), so called because of their simple pitch relationships and their high degree of consonance.
All three of those are simply I-V-I progressions. the V-I is called an authentic cadence, or full close. It's the most widely used cadence there is.
I'm not sure what else I can say about it.
V-I is when the music moves from the Dominant chord to the Tonic. There are arguments that all western music is about how we move from the dominant to the tonic, but that's a huuuuge topic
As for which sets go together, it's all about what key you are in, and the context of what you're playing, and which follows which. (basically it's a way too broad topic, but start by learning about key signatures)
see also:
Assuming that the chords are intended to be read top to bottom, left to right, I would say that you have a I V I chord progression with dominant seventh/ sharp ninth chords.
In this case the seventh is omitted, but the combination of a major and minor 3rd in the same chord (i.e. E G# B G or A C# E C) would usually be called a dominant seventh/ sharp ninth.
This is the classic Hendrix chord in Purple Haze, among other things...
http://en.wikipedia.org/wiki/Dominant_seventh_sharp_ninth_chord
If you are talking about guitar, these are "power chords", usually notated as "5" chords (as in "C5").
Played on three adjacent strings, they are easily movable chords. Move the shape to different strings (e.g., from EAD to ADG) and you get the perfect fourth.
Especially when played on an electric and adding distortion, power chords have a distinctive sound. For examples, see The Kinks' You Really Got Me
Deep Purple's Smoke on the Water
or The Cars' You Might Think
In a general sense, that pattern is simply referred to as "open fifths." (It has other names too, such as a {0,7} unordered pitch class set). Sticklers might argue that this is not a chord at all but an interval with one note doubled.
It's common because the notes are harmonious with each other even in lower ranges. A full chord in the bass sounds very muddy, but leaving it "open" allows the notes to ring a bit clearer. You will see open fifths in the left hand whenever a chord is in the "open position" meaning the notes of the chord are spaced out for a more open sound. Another common left-hand pattern is 0-5-10 (C1,G1,E2) which also has a pleasant open sound but is more difficult to play as it requires your left hand to stretch to a 10th.
So that explains left hand open fifths, but why does this pattern show up in the right hand as well? Well, an open fifth is a lot like a triad that is missing its third. Some chords, however, have their third in the bass (this is known as a 6-3 chord, named after the size of the intervals above the lowest note). When there is a third in the bass it is very difficult to double it without introducing parallel octaves, which is considered poor voice leading in much of western music. So if there is a third in the bass, the right hand is often playing open fifths. You'll find this pattern all over the place in the scores of Mozart and Haydn.
