Download manager's a bit weird - each download belongs to the tab that started it, which is fine and totally in keeping with the "each tab is its own process" thing, but it takes some getting used to since very often you have a tab open specifically to start the download with, and would usually close it once the download's been queued and go do something else. Mostly takes getting used to, except for the fact that if you do close the tab, Chrome just throws those downloads out the window instead of warning you that you're about to terminate them (like every other browser does when you do something to stop the DM).
From what I've seen, if you close a tab from which you made a download (say, a Rapishare page), the download will keep going in the background. To check its progress, you open a Downloads tag by either hitting Ctrl+J or clicking the wrench->"Downloads." From there, you can pull the tab into its own window and treat it like the Firefox download manager.
I've had a download going in both a regular window and an incognito window at the same time and opened download tabs in both after the downloads were started. The incog download didn't show up in the regular download list, but the regular download appeared in the incog download list as "Canceled." Both downloads completed successfully.
If you start a download and completely close the Chrome window, it'll cancel the download and delete the partial file, and when you start Chrome up again the canceled download will appear in the download list, but you won't be able to restart it; your only option will be to manually remove it from the list.