Annoyingly most guitar players seem to 'just play' a rhythm/strum pattern and it sounds like a song.
What advice can the community here give someone who is trying to go beyond playing 4 downs to every bar?
Why do people do this? It's because your basic "4/4" strum pattern is very very boring. Most people are simply going to play something more interesting naturally after a while.
First, since you seem to imply that you can play the "4/4" pattern very well you should have no problem changing it up a little. Start off with small changes.
1 2 3&4
So here we play your standard "4/4" but use an upstroke inbetween the 3 and 4 beats. So, we play twice on the 3rd beat. Very simple change.
You can move the "&" around,
1 2&3 4
or add more
Usually upstrokes are used on the & because it feels more natural.
After that you can leave beats out
1 2 _ 4
Same theory applies with the &(move it around, etc...)
Then you and mix them
1 2 _&4
Again, same thing as before. If you practice this kinda stuff diligently you should now start to be developing some subconscious approach and do these things without thinking about it.
After that you can start doing 4 strums per beat.
You can think of any strum pattern as simply leaving "off"(Actually tying) divisions
so your basic "4/4" is just the above pattern with the 16ths all tied per beat
1e&a2e&a3e&a4e&a 1 2 3 4 1 a2 a3 a4 a 1e 2 & 3 a4 & <- Kinda complex & & & & <- playing inbetween the beats
If using up to 16th notes only then there are 2^16 = 65k possibilities. There are only a small handful that are actually used.
Some things you can do further are add 32nds(these mostly come by feel and you really don't think about them or practice them like you do the eights). Play some divisions/beats stacato. So instead of
1 - - - 2 - - - 3 - - - 4 - - -
where - means you let that chord's beat ring out(e.g., that is your standard "4/4" pattern above)
1 2 3 4
where now we actually just play the chord ON the beat like in "4/4" but mute the strings right after. This is not really practiced much as it is more "feel".
In any case, start with the very basic stuff I mentioned and pretty soon you should be able to make up some much more interesting variations. Once you can do that you can start picking notes out of the chords to make it even more interesting(just pick random notes from the chord instead of strumming the whole chord all the time).
It's all about adding variations/changes to make things interesting. You'll have some people not play the same chord the entire pattern but add some notes from other chords(sort of fills or NCT's). It's all about keeping things interesting.
I think that your fretting hand can be as important to your rhythm technique as your strumming hand.
Fretting hand string dampening
For instance one technique you see a lot across many genres is string dampening, involves slightly lifting your fretting hand and its chord shape on and off the strings whilst strumming with whatever strumming pattern you are using, your fingers should never fully leave the strings otherwise you will be playing the open strings(this may be very well what your after). This gives you a rhythmic damping effect and couples with some palm muting and anything thing else you can think of; it makes for some great rhythm.
Coupling the string dampening with various strumming patterns will work great; any upstroke you play is a good time to lift your pressure of the chord.
A basic and easily learned example of this is 500 Miles by the proclaimers, you can pronounce the technique as much or as little as you would with this song; and its such a basic form; that you can apply pretty much any strumming pattern to it.
Here, you can see it employed in a much more elegant manner.
Working good rhythm chops into your strumming hand isn't as hard as you might think; first off I would recommend getting rid of your pick for a while if you use one (not forever :)), and starting to play rhythm with all of your hand; not just your thumb. A great way to start doing this is to learn some Latin style rhythms, where you are using your fingers and hand in different ways to create rhythms.
Whether you intend to be a flamenco/latin style guitarist or not, those guys have great rhythm; everything you learn from them you will easily apply elsewhere and be a better player for it. Here is a learnable example of what I mean: Rumba Flamenco, - and another with more string dampening
This might seem like going in at the deep end but its really not; in addition to giving you more rhythmic options, using your bare hand is far more intimate than holding a foreign object; having direct contact to the strings will help you develop your rhythmic motor functions quicker.
Good luck; I may come back and extend this answer later when i am less busy.