Apple giving clues?
I think there are a few things to consider when trying to determine the fate of the Mac Mini, and a possible replacement.
1st, when the Mini was introduced (the G4 models), Apple was called "Apple Computer" and their primary focus of the Mini line was to win over Windows users.
Since then, they've dropped "Computer" from their name, and while I think they still want to win over Windows users, their primary focus now is to become a larger presence in the general consumer electronics market.
2nd, Apple is not stupid, and they know how their customers use their products, looking for new features to put into future machines, and to spot trends. So, it hasn't escaped them that a number of Mac Mini sales are being used as media centers, in which their customers are figuring out how to use the machine for a function they never intended.
3rd, if Apple wants to compete in the consumer electronics market, they can't afford to give up the living room to competitors like Sony, Microsoft, and Tivo. And what you find here are various devices with various capabilities with pricing from a few hundred dollars to a couple of thousand.
Steve Jobs has already said that the Apple TV is a "hobby" at this point, and I think that means that he wants to scope out this living room market to figure where Apple can thrive.
So, given all of that, here's my speculation on what Apple may do (FWIW):
The Mac Mini is dead because it doesn't fit the scope of what Apple wants to do anymore.
In its place will be a machine that can best be described as Apple Media Center computer. It will have component, HDMI, and DVI outputs (with an adapter for DVI that allows VGA connection) so you can hook it up to a variety of monitors and newer TV's.
When hooked up to TV's (via component or HDMI), the "Apple TV" Front Row interface is presented (which has already been demonstrated for Leopard), and you navigate through it with the remote control.
If an LCD monitor is hooked up via DVI, along with a keyboard and mouse, you have the new OS/X Leopard interface. The original intent of the Mac Mini line is preserved, by trying to woo Windows users, where they can supply their own keyboard, mouse, and monitor from their older machine.
The "Apple Media Center" will have a DVD drive with improved video capabilites (already demonstrated and announced in Leopard), which will help for TV viewing.
Apple has already expressed a renewed interest in gaming, so if this Media Center will be hooked up to a TV, there will be a need to have game controllers available. So, I expect some type of controller announcement also.
I don't think they're going to get into the DVR market, but rather continue to focus efforts to sell or rent movies and/or TV shows through iTunes, and view video over the web. This allows residual sales beyond the initial sale of the device, whereas a DVR does not (and also complicates setup.)
Because it is a computer, it can be fully networked and find other instances of iTunes (Mac or Windows) on a network so content can be viewed on a TV or monitor. Photos from iPhoto can be fully viewed.
Hardware will be at least a 2.0 Ghz Core 2 Duo processor with an ATi graphics chip (to handle the gaming.) I think there will be two models, differentiated by processor speed, graphics chip, and/or hard drive capability. Pricing will be close to the Mac Mini line now, but maybe a little higher. I think the "low end" goes for around $699 and the "high end" for $899.
The Apple TV line stays for those that don't want the gaming and DVD features of the full Apple Media computer, and want just an "iPod for their TV." But what will be interesting is that the Apple TV can be a "media extender" for the full Apple Media Center. The hard drive capabilities will be bumped up, bugs fixed, and a few features added, but there will still be two models at $299 and $399.
This gives Apple a presence at different price points for the living room, providing more capabilities and power at higher prices, while still offering a computer to convert Windows users.
All speculation on my part, but I think this is where Apple is going (or at least close to it.)