Links in the header (navigation) or in the footer (built by), and sitewide links (links on every page of a site) receive a lot less weight by Google and Bing. So while you can build those links, there's limited value in them when it comes to backlink improvement.
Spend your time and energy elsewhere.
And for the record, if a web host ever put a banner on my site without my approval, I'd terminate instantly. I've seen web hosts put hidden code on clients sites that don't show public, but do show to search engines. In every case that I've seen it, I've advised our client to terminate the relationship instantly and pay elsewhere.
As @zomgmike mentioned, if you're a web designer, clients are generally more than happy to put your link on their site, and you would then cross promote that work in newsletters etc. This is fairly well accepted, but again, not really useful for improving backlinks to help improve site authority/rankings.
We have a number of sites that we've worked on where we negotiated not to put our information on the site, but allow us to use the design in our portfolio. Other sites, we choose not to associate our name with the client as we know they'll destroy the site within days of receiving access