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.