We're currently in the process of adding a double wall oven to our kitchen. We had to cut down the countertop to accommodate the wall oven cabinet and now we have a problem I haven't run into before. While we can easily hide the edge of the countertop touching the back using a backsplash, I have no idea how you're supposed to hide the edge of the countertop touching the cabinet?
How is this typically handled?
Thank you!
Image attached for reference: 
That is handled with caulk. Either black or a color close to the light part of the counter, almond or tan.
I find good results if I apply the caulk. Smooth with a finger, then wipe with a lightly wet grout sponge. like this: sponge
Usually a bead of caulking in your favourite available colour.
Will also seal the joint to prevent any spills from going in/under.
Other answers are good; another other method is to glue a small run of quarter/shoe molding stained to match the cabinet. The cabinet face should be about 1/4" past the cabinet wall; you can get 1/4" molding, so it won't stick out past the cabinet face.
Looks like you have some glue or something behind the cabinet face too, so you can stain/paint that while you're at it.
To a large extent this comes down to 1) how wide & irregular the gap is between the counter and the cabinet and 2) aesthetics/personal opinion.
Here are examples showing both approaches. The first is from a remodel I did some 14 years ago in a previous house, and shows a backsplash used that was made from the same material (granite in this case) as the counter.
The second picture is from a recent remodel we had done where just caulk was used to seal the gap.
I'd consider extending the backsplash forward along the cabinet, if there is one -- or adding one if there isn't. It still leaves you with countertop material abutting wood, but it would at least look more deliberate and be more spill resistant.
