I can think of two similar ways. Both of them use the Solidify and Shrinkwrap modifiers. Model your continents as planes -that is, give them no thickness. You’ll be letting Blender do the heavy lifting for you. Give them a Shrinkwrap modifier with your globe object as its target and position them along its surface. This will curve them around it and make them stick to the surface. Next, give them a Solidify modifier. This will give them thickness and elevation, but only a uniform thickness, too smooth for real continents. From there, you have two possible methods of making mountains and valleys and such. Follow along in this file to see how: continents.blend (1.07 MB)
Continent1 - Create a vertex group and call it something like “Height.” Take the continent object into Weight Paint mode and select that vertex group. Set the mix brush’s strength at something lower than 1 and start painting. The higher the weight, the higher the mountain or plateau. Give the continent’s Solidify modifier a negative Thickness value, and use this value to set the highest possible elevation.
Continent2 - Here you’ll use a UV mapped image as a height map for a Displace modifier. You can just paint onto the image to create detailed elevation, rather than using vertex groups. For some reason I decided to use a white image and paint grey onto it, which means that I’m painting the low spots rather than painting white on black to create elevation, but you can do it either way.
Edit: Obviously your continent meshes don’t have to actually be shaped like a square plane. Their outline can be whatever you want. I just used plain planes because I’m lazy. Just make sure they’re subdivided enough to get the variation in elevation that you want. Only use this for major land features, like the general shape of a mountain range for instance. Use normal maps for the details.