So, I think a distinction needs to be made here. Your title mentions waves, but you refer to boat wakes in your post. Against a breaking ocean wave, you do want to hit directly bow or stern on, because anything else will cause the ocean wave to turn you sideways where it (or the next one) will immediately flip you over unless you are good at bracing. A boat wake is a different thing. The waves from a boat wake are usually smaller, have less energy, and won’t break until they hit an object, like your kayak. I’m going to aim the rest of my post at dealing with boat wakes.
As the wake is coming in, the first thing you can do is angle away from the wake while still paddling in the same general direction you were before. This gives you more time to prepare and gives the wake time to weaken before it hits you. You would only angle away about 30 degrees, just enough to buy some time and let the wake lose some energy without getting too far off your current course of travel.
How you approach the wake depends on your boat and the size of the wake. Ideally, you only want to hit a wake head on perpendicular to the wave if it is lower than your bow. Otherwise, the bow will pierce the wave and the wave will come over the bow and possibly fill the kayak with water. Some kayaks, especially sit on tops built for the ocean like the Ocean Kayak Frenzy, are designed to take waves head on, but in most cases, head on is only good for baby waves of a half foot or less. You can raise the bow of a kayak slightly for a second to make it over a baby wake by leaning backwards if you have a way to wedge your knees against the sides of the kayak or use thigh straps in the case of a sit on top.
You can take a wake on the side, but you need to adjust your body position so that the kayak tilts away from the wave to match the angle of the wave. As long as the wake doesn’t break on the side of the kayak, the kayak will just float sideways over the wave. If you don’t tilt the kayak at all, or tilt it towards the wave, the wave can break on the side of the kayak and soak you. Also, it is recommended that you keep paddling forward parallel to the wave because the faster you go, the more stable you are. Alternatively, if you weren’t moving in the case of the wake surprising you, you could do a brace on the side away from the wave. The wave wants to roll your kayak over away from the wave. So, if you push with your paddle blade against the water (bracing) on the side opposite from the wave, it’ll counter the roll and prevent you from capsizing.
The best option is probably that 45 degree-ish angle that was mentioned. It would be similar to taking the wave side on, but the wave would be aligned with the side of the bow, instead of the side of the cockpit, reducing the chance of taking water into the kayak. So, yes, when I take a wave, I do kind of zig zag. First, I “zig” away from the wave to allow it to dissipate as much as possible. Then, I “zag” towards the wave, lining up the side of the bow to hit at that 30-45 degree-ish angle. You then shift your body weight to allow the kayak to roll with the wave and float right over it.
As far as letting the wave hit you in the stern, I would only do that if I was trying to surf the wake. You wouldn’t be able to actually “surf” the wake like an ocean wave, but you can get a decent speed boost from a series of waves in the wake. Be aware that doing this can push you into the shore. Also, beware that if you slow down by back paddling as a wave hits you in the rear, it can break over the stern and soak you.
One more thing about wakes, be wary of wakes when you are near a bulkhead or other flat, solid object on the shore. If you are too close, the wake can actually hit you, then hit the bulkhead, and then reverse direction back towards you, thus hitting you twice.
Whoa… did I really write all that? Well I hope my ramblings help you in your dealings with boat wakes and other waves in the future.