(I apologize for so many spoiler tags... I suggest staying away from this question entirely before seeing The Force Awakens.)
In what is probably considered to be the most pivotal moment of the movie, we are led to believe that...
Kylo Ren kills off Han Solo.
However, what I recall seeing is...
Kylo appears to have impaled Han, as we can see the top of Kylo's blade behind Han. Han clearly isn't liking it much, and then we see him fall off of a platform. Later, we see Leia flinch when we can presume that Han got the lights knocked out of him (by impacting whatever he lands on). Note that Leia could also feel when Luke was in danger and needing help to survive.
The movie seems to imply a complete conclusion. I also think that out-of-universe comments by key people seem to also indicate that current interpretation. However, we all know how much we can trust Hollywood. Heck, even in the clear-cut case of actual on-screen death, we may never know, as clearly proven from this quote related to James Cameron's (first) Avatar movie.
actor Stephen Lang has hinted that Colonel Quaritch could return for a sequel: "You think those two arrows in my chest are going to stop me from coming back? Nothing's over so long as they've got my DNA." [source]
So, it's quite clear that we can never trust Hollywood. Even within the same series, Star Wars showed us that
Obi-Wan Kenobi may appear after being sliced. Although, in this case, the character did "disappear". Yoda's demise does indicate this means death.
The only supporting evidence I've come up with is that RotJ's Emperor seemed to be "done with" after his final contact with his servant, so falling like that has some precedent of being conclusive. However, given the transformation that Anakin had, which caused him to start having the figure that people typically think of as Darth Vader, the 30-year old Empire has demonstrated substantial medical abilities. If Snoke directed General Hux to do such a thing (clearly without the attacker's current knowledge), what are the chances that the ill-fated character may still be drawing breath? Or, if that seems too speculative to be answerable: how capable would the opposing army be, to try to save the specified life?