Hi, this is a pretty broad question.

Basically I'm just interested to know what people's opinions are on the current best hardware for a server.

Required functions of the server:
#) At least 7TB hard drive capacity in RAID5
#) Ability to hot-swap faulty drives
#) Able to serve 1080p video content to ~10 clients simultaneously
#) Able to serve at least 2 clients simultaneously on LAN

Non-server like functions it will also need:
#) Able to display 1080p video content (ideally through HDMI, otherwise VGA is fine)
#) Able to play 5.1 sound directly
#) Ability to record digital TV (optional if not crazy expensive)

I don't have an infinite budget, so not necessarily looking for the theoretically best server ever, but I am interested in value, and don't mind paying a bit extra for something that is worth while.Personally, I'd be looking at two separate machines - one as a file server, the other as a HTPC, to perform the non-server functions. My reason for suggesting that, is that a case that can accommodate and effectively cool enough drives for the storage you want, plus room for expansion which I assume you'll also be looking for, would by no means be a media chassis, and probably not very quiet. Additionally, the OS plays a large role. I would go for Windows 7 for its media centre capabilites - the media centre is truly excellent. However, to use it as a file server, it might not be the best choice and you may be better served (pun intended) by going for, say, Windows Home Server. As you mentioned, it's a broad question, so it's a broad answer.

The main expense in the system would be the RAID card. They can run very expensive, so what I would actually recommend is a used Dell PERC 5 controller. They can go on Ebay for <£100, you'd also need two SFF-8484 cables, which "breaks" the two SAS ports into 2X4 ( SATA ports. For a little more info on going that route, check out this thread.
If you don't want to go used, I'm not sure what RAID card would be best as I'm very unsure on pricing.
I would advise strongly against going with any kind of software RAID, be that on the motherboard SATA controller or on a software-based RAID card (hostRAID or similar). Software RAID in general is less reliable and much slower, software RAID on a card is a little better than that on a motherboard but I'd still advise against it.

Hot swapping drives does depend to an extent on the way you're plugging them in. You'll probably need a hotswap bay adapter, or a case with built in hotswap bays.

For the drives, if you don't need speed I'd go for the Samsung SpinPoint F3 EcoGreen 2TB drives. They run fairly cool, good storage capacity for the price, however they are 5400RPM so they're a little slow. For more speed but keeping with 2TB drives, I'd advise the Hitachi Deskstar 7K2000 2TB. I'd go for 4x2TB drives rather than any other configuration because although 7x1TB may work out slightly cheaper, you've GOT a higher chance of a disk failure and less room for expansion.

For the motherboard, I would go with the Asus M4A785TD-V Evo, with an Athlon II X2 240/245/250/255 processor. The integrated graphics should be sufficient for HD playback, with a decent processor to back them up. If you notice slowdowns, a cheap ATI 4650, 4670, 5450, 5570, something like that, would ELIMINATE that.

2GB of RAM would suffice for this machine.

For a TV card, I went the Ebay route and got a very nice dual analog/dual digital tuner for about £20. Can't remember the model off the top of my head but it's never let me down.

As FAR as being able to serve video goes, that depends to a large extent on the network capabilties already in place. Assumign you have a Fast Ethernet or better network in place, it should be fine.

Oh - last but not least, the PSU. With a lot of drives you'll need more than you might think. I'd go for a Corsair VX550, but as it's usually only a little less than the 650W, I'd go for that instead personally.

Hopefully this helps a little