Can a creature with shroud be targeted by its controller's own spells?

Shroud is a static ability that prevents a permanent (or player) from being targeted by any spell or ability, regardless of who controls it. This includes spells and abilities controlled by the creature's own controller. There is no 'friendly fire' exception built into shroud.

This is defined in CR 702.18a: 'Shroud is a static ability. 702.18b: A permanent or player with shroud can't be the target of spells or abilities.' The rules make no distinction based on who controls the targeting spell or ability — the protection is absolute.

This is one of the key differences between shroud and hexproof. Hexproof (CR 702.11b) also prevents targeting, but only by opponents. A creature with hexproof can still be targeted by its controller's own spells and abilities. Shroud offers no such allowance.

Concrete example: You control a Gloomhunter with shroud and want to cast Giant Growth on it to pump it in combat. You cannot — Giant Growth requires you to target a creature, and shroud prevents your Gloomhunter from being targeted even by your own spell. The spell cannot legally be cast targeting that creature.

If you want a creature that protects itself from opponents but can still receive your own beneficial spells, look for hexproof instead of shroud.