From reading the current preview of the "Basic Rules" it looks like each ability score is now granted the possibility of being connected to a Saving Throw. In fact, certain classes get proficiency with a saves against a given attribute, such as a Fighter getting proficiency in saves for STR and CON. So instead of Reflex/Fort/Will saves, we have a save for each ability score.
At first glance, I really like this idea. A spell should clearly be able to be "defended" by something other than just DEX/CON/WIS.
However, I looked through the existing spell list and all of spells use only DEX/CON/WIS for saves.
What's going on here? Is this on purpose? Is this an oversight?
Why give Fighters proficiency in STR saves and then not print a single spell that uses that stat? (Note that Web appears to allow an STR "check" but not an STR "save" to escape, though this may be a mistake.)
My driver for this question was the oddity of inventing STR saves or INT saves and then not printing a single spell in the Basic set that used them. Based on the answers below, there are spells printed in the "playtest" set that do use these saves. So there is some reference material for what should be a STR save.
However, the answers below have even more and better information.
Best Answer
Six saving throws instead of three is by design, intended to emphasize the ability scores, and new usages are likely to come up in future expansions.
Why
Associating saving throws with ability scores makes the scores more relevant, or at least come up a lot more often. It has been six saving throws since the first playtest rules.
Quoting the transcript of an early seminar back in 2012:
It has other benefits, such as less terms to learn or more varied defense. But the main reason to deviate from 3e and 4e, despite the costs, is likely for the reason quoted above.
Where
The playtest had spells that are not included in Basic, and among them you can find uses for the other three saving throws. For example, Gust of Wind requires a Strength save, while Banishment and Holy Word ask for a Charisma save.
Apart from spells, monsters' abilities also call for saving throws. For example, in the playtest the Mind Flayer's Mind Blast calls for an Intelligence saving throw from each victim. Or the Water Elemental, when it pushes you, forces you to make a Strength saving throw.
Monsters are not included in Basic for the moment, but should be in the future.
There are also rumours that Intelligence saving throws will be used for psionics, which Mike Mearls appears to substantiate on Twitter: