I've decided I want to get my own domain for a few projects, and also want to rent some hosting for it (as I have neither the equipment nor the patience to host it myself).

Does anyone have any recommendations? I don't need loads of bandwidth or a user database or anything.

Me and Bean0 can both recommend http://byethost.com/
Very cheap, never had a problem with them...

Domains - 123reg.co.uk
Hosting - eukhost.com

Never had trouble with either, customer support on EUK is very good, although they will ring you at 8am when you've not paid your bills!

I'm guessing it's not at all difficult to have hosting by one company and domain by another?

Quote from Crashgate3 :

I'm guessing it's not at all difficult to have hosting by one company and domain by another?

Not at all

(TheStig)hosting.com is pretty good I think? But on a more serious note I'm not really sure what to recommend depends what stuff you need tbh and how much you're willing to pay.

http://servergrade.com/ have hosted all mt sites with them, fully recommended

Quote from aobrien :

http://servergrade.com/ have hosted all mt sites with them, fully recommended

It was the same as we used for SLite, however the company is located in australia, so you will experience slow website loading if youre living somewhere else than down under. Cheap and reliable though so i recommend anyway

£5 a month ill rent u some, No illegal stuff

I'm actually using FreeBee Hosting, which is free 100% add-free, too, and I haven't had any issues with speed or availability so far. Of course, if you're going to be hosting a corporate site or anything that's gonna get thousands of hits everyday I recommend you get a paid hosting service, but if it's just for some projects you're gonna do then they're more than decent enough. It's what I use it for as well. It's got everything you need.

For a domain I use Co.cc which are also free I used to have a paid hosting service and a paid domain but decided to drop it as it was costing me money and I didn't really get anything out of it

I would recommend MediaTemple or DreamHost.