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Think it has been answered but anyway:

You only need a Gold membership to play online or use Xbox Live apps.
Buying games, downloading demos, videos, music does not require a Gold membership.

On every new 360 you can create up to 6 different Live accounts that come with one month of free XBL Gold.
So if you don't care about your online identity or achievements, you can play online for 6 months without paying anything.