What you end up with is the average of all the active signals (even if they're actively silent), rather than the sum, but the only real difference is the eventual volume of the final mix, which you can easily compensate for by turning it up slightly. The resistors prevent the inputs from being shorted to each other, so that none of them go into overload protection, and the technically weaker drive strength is still negligible for the line input that's going to receive this combined signal. The Grounds can all tie together directly.
If you're somewhat decent with electronics, you can build a simple passive mixer with just the appropriate connectors and some 10k resistors from the parts section of RadioShack (or whoever sells them near you):
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