I'm a new Minecrafter, and was wondering if new updates are backwards compatible. Specifically, will the new "Adventure Update" features (Beta 1.8) appear in existing worlds created with Beta 1.7 and earlier? Or will I need to create a new world for this version?
No, ruins and villages are generated with the world, not actively built. If that changes in a future update, then it might not be required then, but for now all new geographic features require you to generate new chunks.
The usual way of doing this is just making a new world with all new chunks, but if you walk to places that you haven't yet, then new chunks will generate. (Potentially with new features.) It's still recommended that you generate a new world though since you might have to walk a while to get to new parts, the boundary between versions might not line up right, and biomes might shift(especially with the addition of a new one), but if you haven't explored much or really like it so far, it might be worth it.
Areas explored prior to the 1.8 update will not contain 1.8 features, but if you have an old save you will still get 1.8 features when you explore new areas("chunks").
If you want to keep your old save and still have new features close to your base you can delete explored chunks with an editor such as MCEdit. Basically you delete all chunks that are explored and don't contain your base or other modifications you want to keep. The deleted chunks will then regenerate the same again, but with added new features.
This is an excellent way when you are running a long lived SMP server where you want to enjoy the latest features close to the core area.
Check my answer in this thread for a more detailed guide to using MCEdit to delete chunks.
By default, worlds created prior to 1.8 will be Survival maps without structures enabled. If you use an NBT editor (like, er, NBTedit), you can enable NPC villages, etc., by changing the value of Map Features from 0 to 1. (You can also toggle between Creative and Survival by switching Map Type between 1 and 0.)
However, even with structures enabled, new map features and new biomes will only appear in chunks that haven't already been generated, which means they only start generating beyond the furthest points that you've traveled. Since I'd explored a much larger space than I'd built in, I solved this problem by opening my world in MCEdit, using the selection tool to draw a big box around everything I'd built, switched to the Chunk Tool, and selected Prune (which deletes all the chunks outside of the ones you've selected). When I opened the map again once I'd updated to 1.8, the new map features and biomes (including, I can guarantee, mines) appeared in the areas outside my selection.
With this technique, the boundaries can be a little bit jarring, so you can use a script like this one to improve things, although I haven't tried that myself.