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: 
Domains are important for getting users to your site, not so much once they are there, that's the time for your interface, design and service to shine. 

A few points on marketing;

**Clarity**

If you are planning to promote it via word of mouth / radio / TV / telephone the domain should be;

1. Phonetic (spelled like it sounds)
2. Easy to spell
3. Avoid hyphens (if you have to have separators, hyphens "-" are preferable to underscores "\_").

**SEO**

If you are planning driving traffic via SEO, if you can get a keyword in there, it helps. 

Be very wary of domain hacks. Domains like "make.it", "dance.in", "lun.ch" may sound cool, but unless your markets are Italy, India or Switzerland respectively, you'll have to work twice as hard in SEO to rank in your local Google.

**Credibility**

Users often perceive as less trustworthy:

1. Overly long domains e.g. "credit-card-interest-calculator.com"
2. Less common common TLDs like .eu, .info, .us etc (rather than .com, .co.uk, .net etc)

**Geographic relevance**

Specific TLDs can be a strong indicator to a user that the service applies to them e.g. "widgets.com" will usually be assumed to be a US site, whereas French visitors will be more like to use "widgets.fr" as they know it's a service they can access. Also the point about TLDs and local domains apply.
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.