With local clients, yes. Local clients want me to handle everything for them. Even if they want to change some text on their site. They call me up or email me to make the changes for them. But, it's okay because they pay more, so I don't mind being their webmaster, as well as host.
For us, no also! We're a hosting company ONLY. All of the other factors of designing, maintaining and programming websites are done by other companies.
When I ran a design company we did have monthly maintenance packages with customers that were more than happy to have it.
If you have the time and can allocate the resources, it can prove to be a pretty nice recurring revenue. Web Design is often considered a ONCE OFF purchase, but if you structure a maintenance and backup package and maybe some analytics or stats etc, you can make a pretty nice package for them.