Consistency

Anyone who publishes in the entertainment medium will tell you that consistency is your most valuable asset.  Reliability is the gold standard of the periodical market.  That, and the ability to draw cats being cute.

Most novel writers can avoid the crunch, given the wide span of time most authors take to pin together a completed work.  A lot more weight is given to readability (and re-readability), since the novel is a singular entity, isolated unto itself.  That said, any author who doesn't think of herself as a periodical is missing the bigger picture.

There aren't a lot of style monkeys left.  Most authors pick a genre and stick with it (many never leave the same setting).  This model has worked for years and will continue to work well beyond the flying cars era.  As human beings, we like being able to predict the future in some small way, so a writer with a consistent form or one who follows the same characters book in and book out feeds the need and becomes beloved.  That makes a wholly different form of consistency valuable to the novel writer.

Personally, as much as I love reading them myself, I don't advocate becoming a slave to the thirteen-book series.  There are advantages in sequels:  greater depth to a setting, a wider arc for your main character or the blending of the two when the environment changes dramatically and it evokes a shift in the characters themselves.  That said, if you're going to keep writing the same character, make certain you leave plenty of room for growth.  Otherwise, you're really just playing dress-up.

If you do plan go in for the long haul, use the same rules for your setting as for the character.  Let it grow and change.  Don't fall into the trap of just filling in the pieces you haven't covered before or you may risk winding up with something clumsy and unwieldy.  You don't always have to expand:  placing familiar characters in a new, linked environment can open up entirely new opportunities in their development. 

Alternatively, removing a stable feature of the world can be as earth-shaking as a dozen new discoveries.  That said, be careful what you set ablaze:  fans have a funny way of falling for the things you might otherwise want to discard.  If you have someone who can give your work a once-over before it leaps into the public eye (and you should), ask them how they'd feel if suddenly the spunky comic relief got speared through the chest in book three.  You may be surprised at what you hear.

Back to the subject of consistency:  any time you plan on building an ongoing character arc across several books in a series, it's important to make sure the character stays true to some original standard.  There has to be some common vein, even in the darkest moments of the character's shift, that harkens back to where they started. 

It doesn't matter if the ace-pilot-slash-swordfighting-wizard looks nothing like the humble farm boy he once was so long as you establish that somewhere deep inside him is a piece that has somehow remained resilient in the face of all this upheaval.  The Simple Savior trope is all too common in any medium, and we will always love it, but the only thing that makes it work is the thin strand connecting the unlikely bumpkin (that is to say, us) to the galaxy-crossing mega-hero. 

The same applies to a character in a series.  No matter how many twists and turns the character takes, never let that strand break.  Find something generic enough and core to the character's being and write it on a little card.  Keep that card with you throughout the series.  Laminate it if you have to.  It will be the thing you audience comes to adore. 

After a few books, any attempt to break that strand will lead to confusion and anger in your audience.  If the writers for MacGuyver had run short on ideas and just said "Okay, fine, he picks up the gun and shoots somebody," the series would have ended long before mullets went out of style.  ...Were mullets ever in style? Nevermind, back to the point...

Your character is more than just a name.  They're an idea.  You can twist and bend that idea, you can run it through the ringer, bombard it with all manner of obstacles and it will come out all the more polished for the effort.  But set aside that idea, sacrifice it, drop it on the floor and suddenly your character is just a name and a quirky pallet of idiosyncrasies. 

In the end, it's all about consistency.