What Robster has said above is perfect. A few other things I would add to that are:
Can you see the Spec of the server that you will be hosted on?
If a company has servers that are of a high spec then the last thing they will do is hide that fact. Any company that has the latest technology will be more than happy to boast about it. If they didnt show the server specs id wonder why.
Can you see your current server status, along with the status of the other servers in the rack?
If your on a server and your site begins to run slowly its always good to be able to check the current condition of the server your on which any good host will have available for you to see. Again I would question why a host would not provide that information. Can you see the current server load / current memory usage / amount of HDD space left.?
Server downtime
The best webhost in the world will have server downtime. The differance between a good webhost and a bad webhost is the time it takes to resolve a server that has gone down. 99.9% of server issues can be resolved by a good host within 10-15mins of them being flagged up.
There is no good excuse for a server to crash every few days. If your with a company that has frequent server crashes then the server you are on is probably overloaded, underpowered, not running the latest updates or running insecure vunerable scripts. move host!!. The only other reason for a server to crash is from the actions of a rogue customer which any good host would only let them do once.
Hardware failure is a very rare ocurrance with todays servers. The most liable parts to fail if any are the Harddrives followed by the PSU's. If you have a company that is dependant on its website ie an Ecommerce site then you really should be on a server with Raid 5 or 10. If a Harddrive does fail when the raid is on raid 5 or 10 your site and the server will still run perfectly if not a little slower while the new drive rebuilds. If you have an Ecommerce site then the server your on should also have a redundant PSU that is plugged in! Most datacenters will charge extra to have the servers redundant PSU plugged in so make sure your host has not dodged that charge. Motherboard and CPU failures almost never happen, if it does happen then go easy on your host as that one is not 20 minute fix
Community forums
Look for a company with a community forum. It doesnt have to be active but it has to at least be there. What good reasons are there for a company not to offer you a place to mix with its other customers??? none. A forum can be set up within 10 mins so there is no good reason for there not to be one. Any company without a public forum should get passed by. Also post in the forums before you buy your hosting, how active is the community? how helpfull is the community? and how friendly is the community?. Have any issues brought up on the forums been solved or been ignored.
Testimonials
Does the company have a testimonials area? Have a read. Do the testimonials have a link to a website? Do a tracert to that domain. Does it go to the correct webhost? it doesnt? WHOOOPPPS! Caught! Email them
Use a bit of common sence when reading testimonials. Some testimonials are so blatantly staged I get embarrased reading them. Company x has been in buisness for a week and has 10 testimonials. Sure!
Support ticket times
Submitting a support ticket before buying a hosting package to "test" the speed of a companys response time is not a good way to check how fast a company would normally respond to a support ticket. Good companys would always put there existing customers before there potential new customers so any test emails would be marked as low priority. If you want to know how quickly they would normally respond to a support ticket then ask there existing customers. If you cant ask there existing customers because theres no forum then move along.
You pay for what you get?
Not always the case with webhosting. If your unsure of the host make sure they have a no quibble money back guarentee for at least up to 2 weeks into your contract. Also where available pay monthly for the first few months. A good host will not charge you any extra when you decide to upgrade to a full years hosting package.
£30 a year or less is Budget hosting. You will be on a server with other budget accounts which means there will be more of them which in turn means there is a higher chance of problems being caused by your fellow server users. This does not mean that your server should crash every few days or anything like that but you should expect the occasional slow period caused by a mass email or an out of control script on another site. Budget hosting should only be used for websites that have no bearing on your day to day life. A website about your dog or a photo gallery from your friends wedding are budget hosting candidates. An ecommerce site or a buisness frontpage is not. For £30 a year you should be expecting up to 1GB of diskspace but no less than 500mb for a budget account. If your paying more than £30 for 1GB or less then your on premium hosting not budget hosting and there should be no slowness on your server at anytime.
Find out if the server you will be on has a mix of account types. You do not want to have your £150 a year eccomerce package on the same server as 15 resellers and 100 budget accounts.
Nothing is webhosting is "unlimited" so if you see that word anywhere in a webhosting companys site then move on straight away as thats an immediate attempt to decieve you before you even get started.!.
I'll add more if I can think of any