Well, you don't want to drown out your nice sound do you?
There are several different approaches to keeping your system quiet and cool, so we'll look at them all in depth.
One of the easiest ways to keep your Myth system quiet is to (basically) throw it in the cupboard - don't worry, this isn't as drastic as it sounds. As your probably know, MythTV (like most bits and bobs of Linux) is highly network aware, and will allow you to run a separate backend and frontend. All of the noisy hot stuff like TV cards, hard drives and Terahertz Athlons can be thrown into the backend and kept under the stairs, whilst you can install a low-powered small machine under the TV. All of the control can be done from the frontend, which will just request TV streams from the backend over the network. The downside of this of course is that you need to be able to afford two separate machines, although it will make expandability much easier further down the road.
There is however an alternative for the cupboard approach. Several CAT5 KVM extenders exist on the market. Such a device extends your VGA, mouse and keyboard cables using CAT5 network cable. You can extend up to 30 meters. I (basjan) personally use two Aten CE220 KVM extenders to extend my Dual Head development box from the hallway closet into the living room. I now only have two LCD screens, a mouse and a keyboard sitting in the living room generating zero noise. I also have an SPDIF cable running to my living room amplifier and a cinch TV-out cable to my TV-set.
If you're using an Athlon XP processor and your kernel is ACPI-enabled, you can use the Athcool utility, which works on all current chipsets, and will often drastically reduce your CPU's operating temperature. Unfortunate side effects can include crackly audio and slow hard disc transfers - YMMV. Some people say that these side effects have been eradicated or highly reduced under the 2.6 series of kernels - I suggest you try it out and see for yourself! A more verbose guide on Athlon powersaving mode is here (the former writer on this page created the script David Greaves/My Tips/Cool Script which may help)
Even if you can't avoid having your quad 30GHz Xeon Myth array sitting under the TV, there are still many ways you can reduce the amount of noise todays power-hungry computers like to kick out. There are many specialist computing companies out there specialising in quiet hardware for use in HTPC environments, and I'll list a few of the products you might want to splash out on:
Fan-mates, or variable resistors to you and I, alter the voltage supplied to your fans. Normal fans runs at 12V, but by lowering the voltage to 7V you will get lower RPM's and thus quieter fans. Air throughput is reduced however.
Fan adapters allow you to replace a high-RPM 60mm fan with an 80mm fan, which can be run at a lower voltage and still shift the same amount of air. By nature of their construction, these are best suited to replacing the 60mm fans on top of stock CPU heatsinks.
Get some bigger fans! This will often involve you drilling lots of holes in your shiny computer case, and so isn't for the faint of heart. The basic crux of the matter is, if you want to shift X amount of air in Y seconds, a bigger fan can do it at a lower RPM and thus will run quieter. Lots of modern HTPC cases opt for a few large fans rather than an array of smaller fans.
Quiet and/or adaptive power supplies can also help reduce noise by a considerable degree. There are some (highly expensive) power supplies that don't use any fans at all, and just use a huge heatsink for cooling themselves, and thus run totally silent. However, they don't do much for the cooling of your case! A better solution I believe are power supplies like the Tru Power range made by Antec. These dual-fan PSU's contain temperature sensors which raise or lower the RPM of the fans depending on how hot your system is. Many also provide "fan only" molex connectors to attach your case fans to; these are also linked to the thermal sensor, and will run your case fans at a reduced voltage unless your system gets too hot.
Stealth fans are fans especially designed to run quietly, and usually come at a considerable price premium over normal fans. Brand names include SilenX and Pabst (most fan manafacturers also have their own quiet fans sub-brand as well), and will usually run at much less than 20dB on standard 12V. Many of these fans have magnetic levitation bearings instead of roller bearings, and the lack of physical contact reduces noise *quite* a bit -- you'd be amazed how much noise is transmitted by physical conduction.
Passive Northbridge heatsinks allow you to replace those pesky little 40mm fans on your motherboards northbridge with a solid chunk of aluminium. Be warned though that these can cause modern northbridges to overheat if there is inadequate airflow in your case! Those of you lucky enough to be using Athlon64 or Opteron systems need not worry about this, because all of the hot bits that used to be in the northbridge have now been moved to the processor. Zalman have a range of northbridge heatsinks, but check they can be fitted to your motherboard first.
Use a cooler processor! Many modern CPU's can kick out a helluva lot of heat and can cause your entire system to become uncomfortably hot. Assuming you're using a hardware capture device (either a DVB card or one of the TV cards supported by ivtv) and a reasonably good graphics card, one of the good things about Myth is that 90% of the common functions don't require a powerful CPU at all, so you can often pick and choose the CPU that runs at the lowest power and heat output. Athlon XP's are a good bet, especially if you can find one with a Barton or Thoroughbred B core. The older (2.8GHz and below) Pentium 4 Northwoods are also powerful and run reasonably cool. I have difficulty recommending the new P4 Prescott chips; they run very hot indeed and (clock for clock) are slower than the Northwood variants. Again, I have difficulty recommending Celerons and Durons but that's mainly due to ignorance on my part - other people will be able to fill you in on those. If you don't intend to buy a new CPU and instead want to recycle anything you have lying around, pretty much anything from a P3 upwards will do you proud.
The only areas of MythTV that benefit from having powerful CPU's are MythMusic visualisations, CD ripping, transcoding and DVD ripping. If you're using software capture from a bttv card, you may also want a powerful processor.
Those of you who know about overclocking may well want to experiment with underclocking and undervolting. This involves reducing the voltage supplied to the CPU core and reducing it's clock speed, resulting in a slower but much cooler CPU. I have read somewhere that Athlon64 chips seem to be exceptionally good at being undervolted - some people have reportedly run their Athlon64's stably at default clock speeds whilst using a much lower voltage, ending up with a CPU that's just as powerful but runs much cooler.
Those of you who are even more adventurous might want to try out specialist chips such as the Athlon XP-M and the P4-M. Originally designed to run in laptops, these CPU's run at a lower voltage but the same speed as their desktop equivalents. Beware however that most motherboards do not support these chips, so make sure you know your onions before you splurge.
Using a quiet heatsink on your CPU will also save your eardrums. This can be as simple as replacing the 60mm fan on a stock heatsink with an 80mm fan by way of a fan adapter as detailed above, or you can splurge on one of the excellent, quiet heatsinks from manufacturers such as Zalman. A cool Zalman solution is [http://www.zalmanusa.com/usa/product/view.asp?idx=33