Here's the thing: Elbow patches are basically silly for most of us. I have had a couple of well-loved sweaters that eventually got thin in the elbows, but this is rare (so rare that a sweater my mom knit and wore in the 1970s still has perfectly nice elbows). If your sweaters are regularly getting that thin in the elbows, either the arms are too tight, or you should take your elbows off the table.
No matter. Elbow patches are appealing, summoning as they do images of libraries and bookish students strolling across leafy campuses.
I've been seeing some particularly fun fall sweater patterns featuring elbow patches, like this one*:
via Karen few stitches a day on pinterest
If elbow patches are unnecessary for adults, they are downright silly for kids, who usually grow out of sweaters before they have time to wear through the elbows. So it goes without saying that the elbow patches on the Grove Pullover from Knittin Little are decorative, but I imagine that any child wearing it is well on his way to writing the great American novel:
If you're actually using elbow patches for mending an existing garment and want a slightly more utilitarian (but still adorable) approach to knit elbow patches, check out this tutorial from the purl bee:
via the purl bee
*I swear I saw this sweater on ravelry, but despite extensive searching for every combination of "cardigan" "rainbow" and "elbow," I absolutely cannot find it again; hence, the pinterest link, which was the closest I could get.