It is unusual to find a site that is invisible in the search engines. I mean, you have to do so little to get a website into Google, yet I found one. Actually, I didn't find it - a client presented it to me and asked what could be done. He said it couldn't be found in the search engines. I didn't believe him, but after a quick check, I found that the website wasn't even indexed in Google despite having been online for more than a year.
Let me explain for a moment why this is so jaw-dropping. Most web developers will submit the work they do to the major search engines as part of their service. They'll either do a direct submission or let the engines crawl the site through links. I link to many of my clients' websites through my portfolio page and that's one simple way to set up an inbound link to a site. So imagine how much effort was involved to have the website NOT be picked up by any of the major search engines. You couldn't even find the website under a specific search for the company's name. That's how bad it was.
Fortunately, with a few changes to the site (there weren't even titles!) and the addition of a few inbound links the site was quickly spidered. It is now found on page one in Google when you search for the company name - which is where it should be. As for other SEO, well, that's for the client to decide.
Search engines owe you nothing. You owe it to your business to ensure your site appears in the major engines. At a minimum, if someone just types in your company name they should find you on the first page of results unless you have an exceptionally common corporate name. (If that's the case, you should really think about talking to a branding expert.)