From all the reports we get in our Xbox LIVE forum section it's clear Microsoft added new checks on their Xbox Live service.

Here's a quote from shanafan the X-S XLIVE forum moderator:
[QUOTE] Ever since Xbox Live came out officially, people who accessed Xbox Live with their modchip on were banned. Live detected the modified BIOS that was loaded, and the Xbox's EEPROM (the unique identity of each Xbox) was banned. However, their Xbox Live account was still safe. So, these banned users got a different EEPROM from various sources, and they were back onto Xbox Live. That has been the way for a long time, and was the way to get banned, unless you used a Xbox Live cheat or was a disruptive gamer. However, until recently, it seems MS is taking extreme measures to stop people with modified Xboxes from accessing Xbox Live, even with their modchip off. [/QUOTE]

The Xbox Live Director of Programming already said a few weeks ago they were working on adding new 'security updates' to LIVE.
At this moment it's unknown what Microsoft is exactly checking when you log-in. There are many things they could check: HDD serial/model, HDD-EEprom match, crc check of xboxdash.xbe, search for specific files on HD (example c:/evoxdash.xbe), specific hacked or modified gamesaves, ...
While the banning does NOT appear to be game specific heinrich found the Halo2 .xbe is also checking kernel and HDD:
0x0041158C, "XboxHardwareInfo"
0x00411594, "XboxKrnlVersion"
0x00411770, "HalDiskSerialNumber"
0x00411774, "HalDiskModelNumber"
etc

It also seems (several days ago already) that many people who got banned previously and changed their EEprom to unban themselves are now banned again. This is probably because MS not bans an Xbox only based on the EEprom, but now probably also based on the HDD info. Team SmartXX proved some months ago MS was already sending HDD info to the LIVE servers during sign-in().
While waiting for more research to be done on these new checks, if you want to make sure you won't get banned best it is best to remove the xbox LIVE account from your modified Xbox console (save it on a memory card first so you can easily restore it).
If you still have your fully unchanged (no F, no homebrew files or modified gamesaves) retail Xbox HD - it *should* be safe to login with it and modchip off ofcourse. That's of course if you never connected to LIFE with your swapped HD 'cause MS might have detected it some weeks or months ago. It's not because they ban now that they only start tracking it now.

Right now it's doesn't seem all modded Xbox consoles are getting banned - but keep in mind they ban with a delay. So if you log-in on LIVE today it's possible you'll only get refused access tomorrow. It also looks like Microsoft only bans actual consoles and not gamertags.

If you want to play Halo 2 or other games against people around the world you can still use tunneling software like XLink Kai and XBConnect of course :-)