The Be’er Moshe (Rav Moshe Stern of Debrecyn) ruled (in 7:46) that it is permissible to set the automated system on one’s phone to ring on Shabbat morning to wake him up. Since the system is entirely automated, and nobody is doing a forbidden act on Shabbat on the person’s behalf, it is permissible, and we do not forbid this out of concern that people might think that he is using the phone. However, the Be’er Moshe adds that one should put the phone at a distance from one’s bed so that he does not inadvertently answer the ring or press buttons when the alarm sounds in the morning.
This applies only to an automated alarm system. One may not ask somebody – even a non-Jew – to call him in on Shabbat morning to wake him up, as he will then be having Melacha (forbidden activity) performed on his behalf on Shabbat. Therefore, if somebody is staying in a hotel over Shabbat and wants to request a wakeup call, he must determine what kind of system the hotel uses. If the system is automated, and the call is made by a computerized system, then one may request a wakeup call, but if somebody at the desk makes the wakeup call manually, then one may not request that he be woken on Shabbat.
This Halacha is discussed by Hacham David Yosef in his Halacha Berura – Amira Le’akum (vol. 1, p. 406; listen to audio recording for precise citation).
Summary: It is permissible to set an automated alarm on one’s phone, but the phone should be placed at a distance from one’s bed. Likewise, a hotel guest may request a wakeup call from the desk if the wakeup system is automated, but not if a member of the hotel staff manually makes the wakeup call.