Fusednetwork.com,
Trust me, its well worth it… and if for anyreason you need ANY kind of support you will have a reply to any question within 15 minutes of ticket.. almost guarenteed.
Honestly its the best webhosting the internet has to offer… A slightly higher price but you get what you pay for.
http://www.hostjury.com check that out

NFSN++

Great shared hosting, straightforward pricing, and fast service in my experience.

For shared hosting, I’m a big fan of NearlyFreeSpeech.NET. They have a cluster backend like the much-hyped MediaTemple, and place a lot of emphasis on redundant systems. But their most special feature is the payment model: you pay for exactly what you use, no more, no less, no fixed fee. So they can be *extremely* cheap for smaller websites. Here’s a nice review:
http://hostingfu.com/article/nearlyfreespeech-net-2-weeks-review
Unfortunately, NFSN doesn’t have cron. You’d have to use something like webcron.org.

For $20/mo, you can get state-of-the-art performance and features with a virtual private server at Slicehost. The downside is that since Slicehost does not oversell at all and buys new servers each week depending on signups, there is currently a waitlist. You also need to manage your own server. Slicehost’s performance is better than any shared web host can possibly offer. Quite a few times, I remark at the speed of a medium-sized site I visit, and after I look them up I discover they are hosted at Slicehost.

https://www.nearlyfreespeech.net/
http://www.slicehost.com/

fusednetwork.com . . .

I have been very happy with this host. Travis has had good luck as well.

Well, being on dreamhost I’m happy whenever it falls down to single digits. Double digits is almost universally bad even if you have a beffy machine with oodles of CPU’s, NFS and etc..

Thanks for the tips! Keep them coming. :)

I’m running on medialayer.com and have never had an issue in the year or so I’ve been hosted by them. You won’t get 500 GB of space, but they are big on not overselling and I have never noticed an issue with the tech end of my website and they have always provided prompt service.

They fit into all of your criteria and run on LAMP (Litespeed), have shell access*, Cron jobs, and access to your DNS records.

* I’m not 100% sure if it is full access or not because I have never needed to use it.

@Fr3d: You want the lowest number possible, obviously, but it can be somewhat “artificially” inflated by NFS, which is one of the reasons Dreamhost servers see numbers anywhere from 1-2 up to 800+!

I’ll be keeping an eye on suggestions here though, because I’m definitely ready to move on when my contract is up.

Actually you don’t want the load average to be any higher than the number of physical CPUs and cores – see Wikipedia entry on Load Average ;)

I have two recommendations:

1) For slightly more-expensive access with a great track record for not going down, pair.com. Downside: It’s a non-root account on a FreeBSD box; there’s some stuff they won’t install.

2) For incredibly inexpensive access, nearlyfreespeech.net. Highly recommended for techy folks. They have a really cool grid custom-built that should keep your site up regardless of the status of any individual server. (IE they automatically shuffle instances between servers for fault-tolerance and load balancing.) Downside: Had some downtime recently during a migration to another data center. NFSN has the approach that you’re only billed for storage and bandwidth that you actually use. No monthly cost at all.