No, proficiency bonuses never stack
Your proficiency bonus can’t be added to a single die
roll or other number more than once. - D&D Basic Rules V0.1 Chapter 1, P. 7
You can only ever receive a proficiency bonus once regardless of how many sources grant you proficiency in it. When picking skill and tool proficiencies granted by a background or class, Players should try to avoid overlapping proficiencies as the benefits are nil
However a proficiency bonus may be increased or decreased based on circumstances
proficiency bonus might be modified (doubled or halved,
for example) before you apply it. If a circumstance
suggests that your proficiency bonus applies more than
once to the same roll or that it should be multiplied
more than once, you nevertheless add it only once,
multiply it only once, and halve it only once. - D&D Basic Rules V0.1 Chapter 1, P. 7
DMs can use this as a way to give a bonus to skill checks based on good roleplay and/or planning.
The Rogue's Expertise feature is an exception
At 1st level, choose two of your skill proficiencies, or
one of your skill proficiencies and your proficiency with
thieves’ tools. Your proficiency bonus is doubled for any
ability check you make that uses either of the chosen
At 6th level, you can choose two more of your
proficiencies. - D&D Basic Rules V0.1 Chapter 3, P. 27
While not allowing proficiency bonuses to be counted more than once, expertise allows a Rogue to double the benefit of their proficiency bonus to two skills (or thieves' tools) at level 1 and again at level 6.
Backgrounds granting a redundant proficiency let you pick a different proficiency instead
In the Backgrounds section of the Basic Rules & PHB, the following rule is listed:
If a character would gain the same proficiency from two different sources, he or she can choose a different proficiency of the same kind (skill or tool) instead.
(Note that, while unclear, this rule may only apply to background proficiencies.)
Custom backgrounds are also an option available to players to avoid duplicate proficiencies due to backgrounds.