My Fitbit charge hr (latest version) does exactly this and I love it. The only trick is that having an alarm on your wrist means that the snooze button is always within reach.
You define multiple alarms on your desktop/mobile, for specific weekdays, synced with bluetooth and you can disable/enable each one of them on the watch, which I really like.
But there are some minor problems with this watch:
1) the vibration alarm is not very strong. If I have an important meeting, I use a fallback alarm clock. There are various complaints on fitbit forums.
2) The alarm lasts only 15 secs and it repeats 2 (or 3?) times after 9 minutes. Unfortunately you can't change this behaviour. Moreover, when I'm dizzy I sometimes confirm the alarm and fall back asleep, which happens too easily while lying in bed...
3) other topic, but annoying: the watch is not waterproof
so always keep a fallback alarm. but otherwise it's a great watch.
I also use it to set alarms as reminders if I have an important meeting or event.
A friend of mine had an alarm that started to roll on the floor :-)