There's virtually no risks. If you're on 9.3+ SysNAND, the Homebrew Channel and its homebrews can only run in userland, so there not any chance that any of your game will be erased. The worst thing that could possibly happen is that you can corrupt your savegames if there's a problem while injecting a save using svdt or any save editor, but personally I use it really often and never had any problems.
Oh, and you can also get a semi-brick if you try to install a "bad" custom theme, but you can fix it by removing the SD card and choosing the default theme, and put the SD back again.
And, a "long" time ago, I saw one guy complaining about screen burns after using a NES emulator.
As you can see, there's not much issues, and any one of them can be easily fixed (don't know how for the screen burns part though), so you can be fairly sure you will not make your 3DS explode by using homebrews.