I'd like to create cartoon looking sun / light shafts that look very close (or identical) to the ones in very well known and loved games like Journey:
How can I accomplish this?
Use stretched particle to get the effect. In Renderer, choose "Stretched Billboard". Change Length Scale as you need. This can be used in both 3D and 2D scenes.
If you are actually into effect stuffs learn Shader. Mostly vertex and fragment shader. Drawing things is not always a solution. Build size increases due to extra artworks. Talking about overall effects. See Hearthstone's gold card effect.
You mention you're using Unity so you can use their official "Sun Shafts" feature; it's built right into the engine: You can read these Unity Docs to get a good idea of what they're capable of and this YouTube video can walk you through implementing it.
By the way, you'll need to download the Unity Standard Assets in order to use then.
This is what we're doing and the results look somewhat like they do in Ori.
You need a texture for your light shaft that loops vertically. This is from our project (hence the watermark, sorry)
You add it to a particle material, and add the material to a Plane primitive. It should look nice and glowy.
Two more steps. One, you stretch the plane really tall. As tall as need be. And two, you animate the vertical offset of the texture via shaders or scripting. This makes the light look alive. Add tiny dust particles for extra finesse.
You could add a sort of fall-off effect too with shader scripting, but that's a more complicated matter.