Of course, it didn't happen, but that would have been fantastic. The story goes that SEGA Chairman Isao Okawa visited Microsoft to push his agenda. He wanted his Dreamcast games to be compatible with Microsoft's then shiny new Xbox. Okawa said that it would be a sort of upgrade path for current Dreamcast owners. It would also possibly help save a dying console.
Microsoft didn't bite. Okawa wanted his games to have the fancy online capability that MS was pushing. Microsoft only wanted online for their games. SEGA was handing over customers, but I'm sure Microsoft didn't want to have to pay to retool their game system for this compatibility.
I wonder if Microsoft would have done differently today, looking back. This would surely have helped them out in the Japanese market.
If you're anything like me, you still look at your Dreamcast fondly. I wonder if this would have helped Sega hold on longer or even succeed. Up for a little Shenmue 2 on Xbox, anyone?