In most cases, yes, it can
There is no rule anywhere that would stop a wizard from casting Mage Armor on herself, and then casting Mage Armor again on someone else.
But not if they're cast on the same target
Combining Magical Effects on page 205 of the PhB says:
The effects of the same spell cast multiple times don't combine. Instead, the most potent effect, such as the highest bonus - from those castings apply while their durations overlap.
Or if the spell says otherwise
For example. the Contingency spell says
You can use only one contingency spell at a time. If you cast this spell again, the effect of another contingency spell on you ends.
In this case, it would not be possible for the same caster to cast it multiple times.