Some of these hacks are HIGHLY DANGEROUS to install and/or use! As an example of what I mean by a danger, a mistake with the installation of some hacks can cause an Error 21 to occur every time the Xbox boots to the hard drive. (I'm not sure if things could be messed up so badly that even game discs wouldn't run either.)

Not only are some of the hacks dangerous to install, but they can also be dangerous to leave on the hard drive even once they are installed. Older font hacks are suseptible to the dreaded clock loop. I only imagine that newer font hacks that boot directly in a modified state could be trouble if a new game resulted in an accidental upgrade to a newer dashboard that prevents the hack from working. The best thing is for a hack to boot the Xbox into a relatively unmodified state so that even if a hack was somehow made inoperable by a dashboard update, the dashboard update would likely not be hindered by the hack, so a saved game exploit could still be used. Such hacks are also the safest to install, because a problem with installation tends to still let the Xbox boot into a relatively unmodified state.

Here's a quick run-down on the safety level of some different hacks:

Easter Egg Exploit ("EEE")
If you have a Kernel earlier than 5713, the Easter Egg Exploit as documented on this page is recommended, at least if you are looking for something 100% safe which is exactly what most people entering the Xbox hacking scene want. It is a bit of work to trigger each time, but it is totally safe to install (at least as long as there aren't other font-based hacks getting involved). Other hacks can be installed if you're feeling more daring (or in the case of an old audio hack, if you're willing to sacrifice custom sound tracks).
Audio hack (for dash 4920 and older)
Definitely-going-to-occur limitation of being unable to use custom soundtracks. However, pretty safe to install as any errors are unlikely to cause the dashboard to not load. However, a lack of A/V cables could cause this hack to break so that the hack won't work, requiring re-installation of the hack to be able to continue to run unsigned code. (How often do you use the Xbox without any A/V cables plugged in, though?)
Quite dangerous to install, but once installed the hack should be pretty stable, except programs (like Xbox Live) looking in C:\fonts\ may have trouble even if the system has no active hacks. (The way to not have the hack active would be by having the system launch a game disc, not an executable from the hard drive, upon bootup.) Also, if a newer dashboard came out, it is easy to imagine problems for UDE2 users.
Older font hacks (designed for Dashboards versions 4920 and earlier)
The worst. Dangerous to install, and also dangerous to leave uninstalled as if the Xbox loses track of time (which will happen if the Xbox is unplugged for some number of hours) then the dreaded clock loop occurs.

Realize that installation of the procedures to run unsigned code as part of the system's boot sequence is dangerous: Unsurprisingly an error can result in your Xbox not being able to boot up normally. Some methods (like UDE2) have certain risks that other methods (like EEE) do not. If you're not using one of the hacks declared by this site to be very safe to install, be extremely careful with this process!

I have personally witnessed Xboxes that have been unsuccessful in loading the dashboard when booting the hard drive. One had an Error 21, and the other simply could not load fonts successfully when using the MechInstaller hack. In both times, MechAssault was still able to boot and so the changes on the hard drive were able to be reversed by me and get the system working again. I do believe I have heard of people unable to even boot a game, though. I suspect that may be from Error 5 or 6 or 13 or whatever error number it is that means that the hard drive is unlocked, and that in the worst-case scenerio one can still boot a game, but I'm not sure. If a hack on this page isn't described by this page as very safe to install, I recommend extreme caution before proceding with a hack!

What may work on one Xbox may not work on another!

Despite these dangers or, in the cause of the audio hack, known limitations, a successfully installed XBE hack is a very nice thing because even the most inconvenient XBE hack (I suppose this would be a hack exploiting the sound track copying of a dashboard version 4920 or earlier) is more convenient than running a saved game exploit every time.

Which hack to use?

The key features to choosing a hack include:

Some hacks that work great on one Xbox won't work at all on another. This has been known to limit the number of usable XBE Hacks down to zero options or just one option for some Xboxes.
Safety of installation
Does the Xbox boot to an unmodified state?
Safety of leaving the hack installed
Could the hack be corrupted if the Xbox is unplugged for hours on end? Does the hack cause a modified state right when the Xbox boots, which could be trouble if the dashboard is upgraded by a game (whether done intentionally, or not)?
Ease of use
No doubt that UDE2 runs unsigned code easier than the EEE hack. However, hacks initiated by the audio copying menu tend to have an easier way to run an Xbox in an unmodified state. Users of mod-chips may not care if UDE2 can run unsigned code more easily because the features of a mod-chip may allow for an easy way to run unsigned code.

The XBE Hacks

XBE Hacks take advantage of known flaws in an official, signed-by-Microsoft executable so that unsigned code can be run. The XBE files exploited by these hacks use a digital signature of fffe0000 so that a kernel will run them. Originally these hacks targetted the official Microsoft-created dashboard, but after Microsoft sealed up the logical holes in the programming logic as they released new versions of their dashboard, the hackers started targetting the executable that updates the dashboard to a new version.

Microsoft seems to have the edge on hackers in this contest over power, as Microsoft can create a new kernel that will insist on using only dashboards newer than a date that Microsoft chooses, and newer dashboards can fix any known mistake that hackers document and use to run unsigned code. However, for older Xboxes, the hacks remain.

Some font hacks (the exception I can think of is the Double Dash) will alter the boot sequence. Realize the danger in this: If a soft modder installs this incorrectly (like trying to run an incorrectly signed XBE file) than the Xbox may not boot to the dashboard. I believe, especially in the case of a clock loop situation or when using UPDATE.XBE, that such a problem may even result in the Xbox not being able to boot official games, so even a Saved Game Exploit will not be sufficient to repair the Xbox. Be careful with these!

Some noteworthy links

Right now these are the XBE Hacks. Some of these may be found at X-S exploits page. Others may be found at X-S forums or "The Usual Places".

Soft Modders rely on using XBE Hacks and/or Saved Game exploits that exploit a commercial game's saved game handling.