Home remodeling is fraught with "A or B" choices that balance so perfectly in the middle that it's hard to know which direction to tip.  In many cases it's just a matter of personal preference.  Classic case:  cut-in your paint or mask the room?  I recommend masking, but if you love freehand painting--hey, who am I to stop you?

It's the same with cutting baseboard inside corners.  You can go either of two directions:

• Coping:  Cut one baseboard straight, at a 90 degree angle.  Butt it against the wall.  Cope the second baseboard so that its butt-end conforms to the profile of the first baseboard.
• Mitering:  Miter one baseboard at a 45 degree angle.  Butt it against the wall.  Miter the second baseboard at a 45 degree angle.  Butt it against the first baseboard's angle cut.

What Conventional Wisdom Says

As Taunton's Fine Homebuilding tells us, "...most professional carpenters prefer to cope."  Carpenters on forums repeatedly recommend coping over mitering.  Gary Katz at This Is Carpentry has a fantastic step by step showing how to cope inside baseboard corners, plus he provides a convincing case for why you should cope.  Katz says:

Wood swells and shrinks throughout the year, depending upon seasonal humidity. Coped joints don’t open nearly as much as miters. Cope joints are also faster to install than miters—the pieces of molding don’t have to be cut exactly the right length; in fact, coped material can be cut a little bit long.

He also mentions that coped joints never have to be caulked, which anyone--fine builder or otherwise--can tell you is a cheating way of covering up mistakes anywhere in your house, trim-related or not.

Another point to add is that mitered joints can open up even upon installation (not just over the course of years).  This happens when you smack in those last two nails closest to the joint.  Sometimes they will force the baseboards tighter to the wall, thus widening the joint.

You'll probably be surprised to hear me say that all of these things are true.  But there is a case to be made for mitering those inside baseboard corners...

Just Relax:  Why (and When) You Should Miter Your Inside Corners

1. You Probably Don't Have Wood Trim:  With the onslaught of polyurethane and MDF products on the molding market, shrinkage is a moot point.  Poly doesn't expand/contract, and MDF doesn't under normal conditions (but notoriously will mushroom up with direct water contact).
2. Miters Are Easier To Make Than Copes:  If you have an electric miter saw, nothing can be easier than locking it to the 45 degree angle, pressing the baseboard against the fence, and sawing down to reveal a nice open angle.  By contrast, copes are tricky and take practice.  Most homeowners will be finished with the room by the time they have mastered the learning curve.
3. Miters Can Deal With Out of Square Walls, Too:  One argument for coping is that coped trim will accommodate corners that are not perfectly 90 degrees.  True.  But miters can also accommodate corners that are +/- 90 degrees.  Solution:  rather than slavishly cutting the trim to 45 degrees, cut it to fit.   Adding or subtracting just one degree can work miracles.
4. Wall Angle and Height Help To Hide Imperfections:  The visibility of crown moldings means you should step up your game a bit and either cope it or miter it to perfection.  But baseboards, being at floor level, are far less visible.  Not only that, the joint is slightly shadowed, since this is an inside corner.  
5. Be Real; You're Not a Fine Craftsman:  Katz says that "coping inside corners is a sign of craftsmanship."  True again.  But to get true craftsmanship, you should hire a craftman.  Or make the commitment to prioritize fine craftsmanship over other things in your life--and in your house.  Most of us need to expedite the trim project so that we can move onto basements that need finishing or house exteriors that need painting.  Mitered joints are the quickest way to get this thing done.