Is it too much trouble for you to also include that valuable piece of info?
That said, yes- many of them do let you attach a HDD (via USB or ethernet), or connect to one elsewhere in your home network, wireless or otherwise.
My personal opinion of file access via Wii's homebrew offerings is do not bother. Find a better supported way to access your media collection. Make sure you get the media box that reads the file types/codecs that you need as well. For example, my WDTV Live can read/play back nearly anything I throw at it, regardless of how outdated the user interface can look vs others.
I have purcased a media player and was wondering what would be the best way to connect it to my tv via the hdmi so that I can watch movies on an external hard drive. my usb on my tv only recognizes mp3 and jpeg so I think that the media box is the only option. Or can I somehow connect an external hard drive through my wii with homebrew?