After deleting an app, can you (much) later reinstall it and restore its data from iCloud?

I have several games that, combined, use up a pretty good chunk of my iPhone's flash. I haven't played some of them for a while, and would like to remove them. However, at least before iCloud, deleting an app also deleted its data. Since I may go back and play them again, I'd rather not lose said data.

After backing up to iCloud, can you delete an app, and (possibly much) later reinstall it and restore your data from the iCloud backup?

The answer is yes and no.

What happens quite easily after a restore (for example after an update) is that iTunes restores the save data for all applications, but not the applications themselves. Therefore as soon as you install them, the old save games will be available (this applies to all apps, not just games). Just by itself nothing will be saved without backup.

BUT: If the application supports iCloud sync and stores it's data in iCloud (which has to be explicitly supported), your data will be still available after deleting and reinstalling the app.

In short: You should be really careful and unless you're absolutely sure the application in question does support iCloud for your saved data, don't delete it without backup.

There is no general answer to this question as each game app is highly specific with regards to where the game progress is stored. On some games such as Candy Crush, the score is stored locally on the iPhone unless you connect to Facebook at which point, the game progress is automatically transferred and saved to a cloud account associated with your Facebook profile. I think the case is similar for Clash of Clans.

Having said this, if your game(s) happen(s) to store the game progress locally on the iPhone, you can back up the progress like instructed here (using a free PC iPhone-app explorer): How to backup iPhone games and transfer game scores to another iOS device

You can also restore the game and the progress to another iPhone when you feel the need to play.