"Sonic Ether's Unbelievable Shaders" is probably the most aptly-named mod I've ever seen.
Top image from Sonicether
There are plenty of mods for Minecraft that change the look of the game, like texture packs that add more detail to the blocks. However, easily the biggest change comes from the shader mod, and Sonic Ether's shader pack for that mod. Shaders completely change the way lighting works in the game to use the more realistic effects you'd see in modern big-budget title. We've written about the mod before, but the latest update is really amazing.
image from awsomemaster0101
The latest version of Sonic Ether's Unbelievable Shaders adds new realistic looking clouds that, unlike other mods which add a static image to the sky, are randomly generated. If that wasn't enough, when they cross under the sun, they cast realistic shadows on your world.
image from awsomemaster0101
Image from Sonicether
Image from Sonicether
Another impressive addition are the rain effects. Instead of the vanilla rain effects, which are just some 2d particles coupled with sound effects, with SEUS, the rain actually wets the ground and creates reflections and puddles.
Image from Sonicether
image from awsomemaster0101
image from awsomemaster0101
As an added bonus, the guy who recreated Spirited Away in Minecraft just released a video of the map using a shader mod (although it isn't the latest version of the SEUS pack that you saw above):
If you want to try out the mod for yourself, first, be warned that it's pretty resource intensive, so it'll really eat into your game's performance on an older computer. You can find instructions to download and install the shader mod here and the SEUS pack here.