To celebrate its 15th birthday, Google decided to share a neat Easter egg showing how Google used to look in 1998. To see it for yourself, simply search for "google in 1998" (without the quotes). Sadly, you can't do an actual search on 1998 Google.
Links still matter today for the same reasons that they have always mattered: they send traffic by making connections. Yes, they are still a large part of ranking, but depending on search engines as the only route to your site is a bad idea.