Water in 16 bit games are usually rendered in different ways. In 8 bit games, just make the background blue.
But with the added fidelity, they had to step it up.
Here's a thread on the various things that are done.

In Super Mario World, the water in some levels seems transparent, but it actually uses dithering to create fake transparency. The SNES COULD do transparency, but the level wouldn't be able to have a background, as shown in image 3, a prerelease image showing said transparency.

In Megaman 7, the water is truly transparent, and is by default, yellow. After beating the miniboss, the "water" turns purple and the surface changes. The surface then becomes bubbly.

In Wily Stage 3 of Megaman 7, the water returns, being recolored blue. However, this only happens in various releases of the SNES version and is more commonly yellow. The water will do the same exact transition to purple, meaning the water will instantly go from blue to yellow.

In the Genesis/Megadrive Sonic games, water is done in a very interesting way. There is an alternate set of palettes for underwater. This means that you can make all the colors look anyway you want underwater!
In the REV01 version, the water also distorts the background!

Sometimes the easy route is taken and it's just an opaque blue background with an animated surface