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Mage Armor sets the target's base AC to 13+Dex. Shield gives you a +5 bonus to AC. If you cast both on yourself, does that give you an effective AC of 18+Dex while both spells are in effect?

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Yes.

Bonuses in 5e are rare, and we don't know all of the details yet, but there is no reason to think that Mage Armor and Shield do not stack. The only thing we really know is that casting a new concentration spell breaks the previous one. Neither of these spells are concentration spells and thusly they would not conflict in that way.

5e does not use named bonuses as far as we can tell (preferring Advantage most times other editions would use a named bonus), and really Mage Armor is not a bonus, it's a set amount of AC. The key point on these two spells is that Mage Armor affects your base AC whereas Shield is a bonus to your AC. In this case there is no potential conflict between the spells as far as bonus/base rules go.

The other potential source of conflict would be if two spells did not stack. Thankfully the basic rules have us covered there:

The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don’t combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap. (Basic D&D p 81)

Since Shield and Mage Armor aren't the same spell their effects can overlap just fine.

So yes, they stack.

Caveat: again, we don't have the full PHB and DMG yet so there may be bonus stacking rules outlined in those volumes that are not yet a part of Basic D&D (I've just done a search). There are limited rules on bonus stacking so I'd assume that all bonuses stack for now. The only exception is proficiency where we have clear rules on the subject (it can be multiplied and divided, but never stacked). Proficiency is the only bonus stacking ruling given in Basic.

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Yes, the key point is that mage armor replaces your "base" AC, and Shield is a "bonus", bonuses add/stack, and bases get replaced. Also you should mention the rules about spells stacking unless they are the same spell. –  GMNoob Jul 15 at 12:25
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My hope is that 5E does not introduce named bonuses and does not introduce rules that prevent bonus stacking but instead keeps bonuses very rare. Being able to creatively stack synergistic spells has lots of fun potential, provided they aren't so common that it is easy to do it all the time rather than having to be conservative with it. –  DampeS8N Jul 15 at 15:30
    
@DampeS8N that is my expectation as well. Bonuses that are rare enough that they should stack. –  wax eagle Jul 15 at 15:33
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