Figuring out the key

The alignment is poor, sorry.

The key is C. Em is the iii chord of the key of C. So your progression is V I iii. You can use Dm, F, Am or B. You can even make a momentary key change to anything you like. Just listen to how it sounds.

Here are the natural major keys and the chords in them.

I ii iii IV V vi vii
Maj m m Maj Maj m 1/2 Dim.

C D E F G A B
G A B C D E F#
D E F# G A B C#
A B C# D E F# G#
E F# G# A B C# D#
B C# D# E F# G# A#
F# G# A# B C# D# E#
F G A Bb C D E
Bb C D Eb F G A
Eb F G Ab Bb C D
Ab Bb C Db Eb F G
Db Eb F Gb Ab Bb C

I wouldn't be so sure about the key of C. My money's on the key of G.

As the OP noted, the easiest way to find the key is to identify the chord of resolution. But resolution implies a preceding tension - usually a dominant chord type - and this progression doesn't have one.

That makes identifying "key" a bit harder. But we can narrow the field by doing it in two steps.

First we look at the tonality of the piece: what notes are being used. The chords are:

G: G-B-D
C: C-E-G
Em: E-G-B

Line up all those notes to form a scale, and we get B-C-D-E-G. There are no A notes, and no F notes, in any of the chords.

Assuming we're in a diatonic key, which isn't a big leap given only these chords, the F could be natural (key signature of C) or sharp (key signature of G). And the A could be flat or sharp, which won't equate to any of the standard major or minor keys. So now we can guess it uses one of four scales - I'll start each one from A:

1. Ab-B-C-D-E-F-G
2. Ab-B-C-D-E-F#-G
3. A-B-C-D-E-F-G
4. A-B-C-D-E-F#-G

Only two of those (#3 and 4) equate to major/minor keys - #3 is the key of C or Am, and #4 is the key of G or Em.

I could get into modality and all that, but I'll spare you :)

The reason I think it's in G is that a plagal cadence (C-G) is pretty common, and that would make the Em the vi chord - also very common. And in that case, your other common chords would be Am, Bm, and D7.

From what you've got so far, I'd also go for G as the more likely key. But the fact that there's no V7 - I progression present in either C or G gives you an opportunity to establish either of those keys depending on what you do next. It would be quite easy to make C the key if you include the chords F & G7 in the follow-up chords, whereas D7 would more or less ensure that everyone hears G as the chord of resolution.
It wouldn't be so easy to make Em the key, though, as you've already established quite a 'major' feel to your song.

True, G could be a likely candidate. I stand enlightened. :) I thought of C because there are no sharps, suggesting he could use F, Dm, Am or B if he wanted to. Could be a coin toss.

That inverted G chord gives the G-C motion added V-I power, for what it's worth -- the "ti-do" bassline could carry a lot of weight. Yet the move back to G counters that.

Still plenty of room to establish the progression in E minor or C, or elsewhere. Sit on a chord long enough, and you're in that key. :) Bassline motion however can have strong implications for key center as well.

I recommend sitting in a quiet room and playing through what you've got, slowly & repeatedly, until the key becomes clear in your imagination or until you're sick of it, whichever comes first.

That inverted G chord gives the G-C motion added V-I power, for what it's worth -- the "ti-do" bassline could carry a lot of weight. Yet the move back to G counters that.

Or completes it - we have no idea what the duration of the chords are, and a mi-fa-do bassline is perfectly plausible.

That inverted G chord gives the G-C motion added V-I power, for what it's worth -- the "ti-do" bassline could carry a lot of weight. Yet the move back to G counters that.

Or completes it - we have no idea what the duration of the chords are, and a mi-fa-do bassline is perfectly plausible.

Of course. At that point in the somg, presumably it's not cadential motion or key-definitive in either case. Lacking a more complete chart, we don't know much. Bassline could carry a lot of weight, but no more than chord duration -- probably less. They are factors, two among many.

This seems more about composition than theory per se. There is value cor a composer in knowing tonal theory, harmony & form, as it can tell you something about how your note/chord choices will affect how listeners perceive the piece -- but composers cannot be bound by theory. And I recommend our composer spend some good time with his chord progressxions & see what they tell him about the direction of the piece.

Melody could have a hand in the key as well. If the melody line (let's say a vocal line) contains an F# note it, the total key could lean more towards the key of G.

Some great replies there. Thanks very much.

I've played around with it a bit and have added a change, which is G A5 Em. So I guess it's G. But given that Ive used A and not Am, does that change things? Does that mean the A5 is "out of key"?

Does that mean the A5 is "out of key"?
A5 consists of I-V, so it is neutral, as it is the iii that gives a chord its quality as, either, major or minor. It would be out of key if you were playing in Bb, as A would be a diminished chord.
G - B - D
A - - - E
E - G - B

That A5, in other words, is "in key" in G OR C. Still plenty of room to establish a key center -- and no need to hurry. To delay resolution can create tension, which can be effective. Think of "Lowdown" by Boz Skaggs. You don't get a convincing resolution to a I chord until the little horn break. (We can quibble over analysis of anything, but that's how I hear it.) Compositionally, there can be great beauty in ambiguity. Just be aware it's there.