I can't give a whole lot on strictly gaming, as I do everything with my rig. And for LANs, if they were to happen, I don't mind the weight. These features may not be applicable to just gaming, but forms of them may.
Size
I prefer for all intents and purpose, a full tower. Or larger mid-size. Enough room for excellent airflow, large heatsinks and videocards. A little extra wide would be beneficial, to allow a lot of organization behind the motherboard.
Looks
Black, black interior. Steel gray looks incredibly dated any more, and makes even managed wires stand out and look ugly.
Rectangular side window only, not showing the HDDs. No one is really interested in those.
No ridiculous looks. My only gripe with my 1200 is the top and side window, only cause of the mesh. Not "rugged" looking, but not boring. I like the mesh grilles in front, the size, etc. I'd prefer the classier looks of the P Antec series, but I do not have the bank for them or skills to add windows.
Function
3 5.25 bays. Enough for minimum one optical drive, and two optional things like front audio panels and temp sensors. In my case, two opticals as I do a lot of disc-disc copying. (don't want hundreds of authentic cd's sitting in my car at work or school)
No proprietary fan power grids/etc. For example, one molex off the PSU feeds one large strip that can power devices plugged into it. Just one more link to break, one more part to get in the way, and generally makes wires look more cluttered.
Room for minimum 3 HDD, with brackets for SSD use. Two for a RAID, and a third for media. Full tower/mid could obviously have more. As someone suggested, removable brackets if the user wants to W/C with internal RADs.
Bottom mount PSU. I feel PSU manufacturers will start making the ATX and ATX12V longer as bottom mounting becomes more common place. I just like the weight being at the bottom, easier to keep cooler.
Thumb screws for nearly everything.
Removable mobo tray. I never had experience with one, but enough people ask for them.
No "tools free" stuff, unless it's a thumbscrew. Tools free from my experience has been one more step to the building process, one more part to lose, one more part to break. Lucky the case is still usable when a part breaks, just takes more time. No thanks.
Wire management holes everywhere. Underneath the mobo, above, all the way down the side. Not just one hole either, individual holes. if possible, some on the left side, for wires such as front audio wires or firewire wires. Holes in the mobo tray to allow them to snake up and around? And for larger mobos, provide holes as well. Holes by drive bays, for power and data cable.
Brackets to support the weight of larger videocards against the chassis. Beneficial for gaming if people plan on moving to LANs. Last thing you need is a 300 dollar card biting the dust from a connection snapping.
Cooling
At least a side fan, two rear fans, 1-2 large diameter fans on top, room for intake fans. Provide a few fans at least. Enthusiasts will know what they need and want. Bottom fan for the more VGA oriented setups to help with the side fan.
Enough PCI slots for a minimum of 6 PCI cards. VGA you figure takes two, then sound card, then raid card, then NIC. Depending on the mobo layout, you want those components to be able to breathe and organize wires to and fro with ease.
Front USB, Audio, with wires long enough to be hidden and still reach wherever a mobo manufacturer decides to place their plugs.
Easily removed filters on any intake spots.
Sorry for the lack of organization, I am just thinking off the top of my head. I know some of these aren't completely relevant, but I do not strictly game or require massive VGA processing. I also like the looks, space, and cooling of a larger case. -shrug- Hope some of this is applicable or useful.