I enjoy non linear games but some might as well not include a story line. By the time I feel like doing another story mission I have no clue anymore what it was about. Worst offenders are AC4, Skyrim, Saints row. (Is there a story in Saints row? I can't remember)
Some progression through the world is needed, like the Fallout series, RDR, Ni No Kuni and best example Dark Souls. Or a mix between linear and non-linear gameplay, like Deus Ex: HR or The Witcher 2.
For a strong story you better stick to linear progression. Which doesn't mean it can't have open level design and exploration, The last of us did a great job at giving you freedom on a tightly controlled narrative path. Plus it's also nice to know you'll be rewarded with a new area instead of retreating familiar ground.
Actually thinking about linear and non-linear games it occurs to me that a lot of linear games have better non linear ways of dealing with objectives then missions in so called non linear games. AC4 story missions are about as on rails as you can get.







