I'm no pro in music theory, but I feel like listing down some of my favourite chord progressions in no apparent order.

I will write everything in the C major/ Am scale, as it contains no sharps or flats (except for some cases)
Also, I'm not going to use more complicated chords, that's for you to do yourself... Cause these more complicated chord progressions are easily derived from these simple ones.

So... First progression:

***1: Am F C G

This one is extremely common. Honestly, I do like this, but I try to avoid this. It's the overused progression that Newgrounders overuse.
This sounds nice because it follows the circle of 5ths really well. The F leads to C and the C leads to G.
Despite this being in the minor scale, it does sound happy. That's because all the other chords are major chords.

**2: C Am F G

Another overused one. This one's in major, and it sounds pretty good. Gives a happy sounding song.

3: C Bb F G

This is based on the previous chord progression, except the minor chord is swapped out to a chord from the Cm scale. Honestly, this sounds great. Play it slowly, it feels emotional. Play it quickly, and it becomes a really happy tune.

**4: C G Am F

This is similar to number 2 too, but has a bigger difference.. Sounds happy, but the last chord kind of changes the mood.

*5: Am G F G

This sounds sad, I really like this one, but I think I'm overusing this already.

6: C F Am G

I like this one too. But I overuse it myself. o.o It just sounds damn plain happy.

7: Am F Dm E

This sounds spooky. I especially like it when the last chord is a major instead of a minor chord.

8: F G Am G

I like using this. It really steers away from the two possible end chords, C and Am. It has an epic feel to it.

9: F Am C G

Similar sounding to the previous one, but this has a more sadder feel..

10: C G Am Em F C F G

This is a pretty long chord progression.. If you play it, it is instantly recognizable as the progression used in the song Canon in D. (though it's in the c major scale o.o)
Yea, avoid using this one unless you have a really good melody for this, or you song will sound like a remix of canon.

Well, I think this can get a lot of people started on chords, but I do tell people, if the chord progression is common, I recommend they make the song unique in another way, like giving it a good melody.

And I placed a star beside the most commonly used ones. Like this one. ---> *

So 3 stars means its extremely common, 2 stars means slightly common, 1 star means it's still encountered once in a while and no stars means its rather rare.