Live Chat help seems to fix just about every single problem we have on the fly, and they open Tickets when it gets more complicated, with thorough and fast follow-up.
I have never been happier with my hosting support, and I've used company after company over the years. I've now been with Rackspace (Sites and Cloud Servers specifically) the longest.
I should note that I ended up with them because they took over SliceHost (also great support), so I didn't really "choose" Rackspace based on anything, but loved SliceHost, and the transition was seamless, and the great support seemed to follow.
Why? Because we're such an important client, that they want us to have a more personal relationship, by forcing us to interact over the phone. I wish I were kidding.
Rackspace has folks that know how to fix a complicated issue on RHEL stack at 3am, which is nice. And, unlike a cheap host who has an SLA that guarantees 100% uptime but only refunds you for time lost, Rackspace's SLA incentivizes them to fix things ASAP. Things like a dedicated box having a hardware failure will be restored in an hour and they credit you 5% of your monthly fee for every hour over that. Or 5% for each 30 minutes of downtime due to data center issues (power, network, HVAC, etc). And they do make good on it.
Rackers are a smart bunch, their first-level chat support is great for the million minor issues I need solved. ("We've got a noisy neighbor, can you check it out?", "Can you move this VM to a new host?", etc.)
That's 10 seconds of divided attention required from me vs 10 minutes of dedicated attention for a phone call.