Python, 38 34 bytes

lambda s:s==sorted(s,key=`s`.find) 

Thanks to @xsot for golfing off 4 bytes!

This expects a list of singleton strings as argument. Test it on Ideone.

Python 3, 38 34 33 bytes

lambda s:s==sorted(s,key=s.index) 

This expects a list of digits or singleton strings as argument. Test it on Ideone.

Thanks to @xsot for golfing off 4 bytes!

Thanks to @immibis for golfing off 1 byte!

Python, 38 34 bytes

lambda s:s==sorted(s,key=`s`.find) 

Thanks to @xsot for golfing off 4 bytes!

Test it on Ideone.

Python, 38 34 bytes

lambda s:s==sorted(s,key=`s`.find) 

Thanks to @xsot for golfing off 4 bytes!

This expects a list of singleton strings as argument. Test it on Ideone.

Python, 38 bytes

lambda s:list(s)==sorted(s,key=s.find) 

Test it on Ideone.

Python, 38 34 bytes

lambda s:s==sorted(s,key=`s`.find) 

Thanks to @xsot for golfing off 4 bytes!

Test it on Ideone.