Does Stifle stop a morph creature from being turned face up?

Turning a morph creature face up is a special action (CR 701.33), not an activated or triggered ability. Special actions are not placed on the stack and therefore cannot be targeted or countered by Stifle (CR 116.2b). The turn-face-up action itself will always resolve.

However, many morph creatures have a triggered ability that fires when they are turned face up (e.g., 'When this creature is turned face up, …'). Those triggered abilities do go on the stack and can be countered by Stifle (CR 702.37d, 116.2b).

So the creature will successfully become face up regardless — Stifle cannot stop that part. What Stifle can do is counter the 'when turned face up' triggered ability, preventing its effect from happening.

Example: Your opponent pays the morph cost to turn their Exalted Angel face up. The creature flips face up immediately as a special action (Stifle cannot stop this). The 'When Exalted Angel is turned face up' trigger goes on the stack — you can Stifle that trigger to prevent its effect, but the Angel is already a 4/5 flyer with lifelink.

In summary: Stifle cannot stop the act of turning a morph creature face up (it's a special action, not a spell or ability), but it can counter any triggered ability that results from that event.