Let's be real here - storing your console games on a hard drive has shit to do with "backing them up." More like "keep playing after you trade them in to GameStop."
OK, yeah, they also load and play faster. But whatever your objective, sister site Lifehacker found a new hack that allows you to rig a hard drive to your Wii - even if it has the 4.0 System Menu installed (previous hacks called for an icky downgrade to get around that.) Just a warning, this requires hardware in addition to the hard drive, a suite of mod software, and the know how to use it. And also the willingness to muck around in a Wii and risk melting its graphics card, if a boldfaced "public service warning" is to be believed. The process is lengthy, so be prepared to kill an afternoon. But it is doable.
How to Store/Load Wii Games via USB Hard Drive on System Menu 4.0 [Mike & Heather, via Lifehacker]