Would you rather talk to a live agent or take matters into your own hands through self-service? As with most things in life, the correct answer is "it depends". It depends on the nature of the transaction (eg, sales, customer service, technical support, etc.) It depends on the accessibility / usability / availability of self-serve options. It depends on your personality. It depends on your technical proficiency. And frankly, a lot of it depends on your age.
Self-service is really an umbrella term that covers solutions such as websites, kiosks, and phone systems. Each self-service channel has its pros and cons. Websites are great for performing complex transactions (assuming the user has a computer, knows how to use it, and can figure out the website). Kiosks are great for delivering information and performing simple transactions (such as "information desks", dispensing tickets, processing digital photos, the ATM, etc) but obviously the kiosk requires the physical presence of the user. Phone self-service is widely accessible (because everybody has a phone), but is limited to information delivery and relatively simple transactions.
While self-service isn't necessarily a channel into the contact center, its role in the overall customer experience is critical. For businesses to thrive, they have to let customers engage through whatever method they prefer … and sometimes that is through self-service. Too many businesses try to use self-service as a shield … as a way deflect customers from the contact center. Since many customers would actually PREFER to self-serve ("I just want my balance.", "When is my account due?", "What's the status of my order?", etc), it's great to give them the OPTION to self-serve.
Businesses need to think carefully about how "moments of truth" are going to be delivered to their customers. No doubt customers can be made deliriously happy by hopping on your site and placing an order, but if you make self-service the ONLY option they're likely to look for a provider elsewhere. Offer self-service because it's better for your customers, not because you think it's better for you.