Question: Is it important for the domain of a website to be chosen so that it is simple to type?

For example, consider delicious-dot-ly (`delicious.ly`).  

Would it be fair to say that the difficulty of typing this domain name leads to a bad user experience?

Answer: 
Yes, there are a few considerations for domain names: 

* **Is the name memorable?** Could your domain name be confused with another address, such as goggle.com vs. google.com?
* **Is the name easy to relay?** Can you tell another person the name by saying something like "penny-dash-arcade-dot-com"?
* **Is the name accurate to your brand?** If your site is "Cheap Pens Now", it better be located at cheappensnow.com!
* **Is the name unambigious?** All I have to say is "penisland.com" -- PEN ISLAND, you perverts! How about expertsexchange.com? Y'know, Experts Exchange...

Most of these concerns are strictly branding related issues, and if your service is that good, like bit.ly or del.icio.us, people will forgive quite a bit -- as long as you get the rest right!
Yes, I would say that a domain name is part of the user experience of a website. If a website has a domain name that is harder to remember or type, it makes the user's experience a little more difficult.

Depending on what company it is, it is usually not up to the UX designer. Our clients usually come to us already having their domain name. Of course, we are able to give suggestions, but this is something that a client typically would not want to change if the website already has a lot of users.