Like anywhere, Alice Springs is usually a pretty safe place.  You won't get shot by a drug gang as a result of being in the wrong place at the wrong time.  Nor are you likely to suffer a terrorist attack.

From time to time, Alice Springs does get a bad wrap from the media for crime, however it is generally a safe place - so long as you don't leave your common sense at home! It is important to keep things in perspective - there is crime in all communities, but Alice Springs seems to feature in the media more than any other Australian town of its size.   

if you decide to head out at night - don't walk home in the dark alone or in a small group.  Call for a taxi.  The most expensive taxi fare in Alice Springs is about $30.  Generally it will cost you about $20-$30 to get to most destinations in Alice Springs.  Often there are people walking at night to their accommodation - it's obvious that these people are tourists so they are easy targets.

The main reason that people get themselves into trouble is their lack of common sense.  Recently there were some international travellers who left their car - full of their belongings - in a small carpark in the north part of Alice Springs.  This carpark, whilst busy in the day is totally vacant at night.  Their car remained there for nearly 8 days, and was broken into and stolen.  They lost all their belongings - if they had have left their vehicle in a more sensible location, then they wouldn't have had half the issues they encounted.

Remember too that you are in the desert. Remaining hydrated is really important; and with water, not beer! There is a story of a traveller in about 2007 who was rescued by local police twice when he got lost walking north east of town. He was lucky he was in mobile phone range, but he hadn't let anyone know where he was walking, was not carrying enough water, and got lost. Not satisfied with getting lost once, he went back the next day to look for his shirt. The police were less than impressed!  

 So, use your common sense and have a fantastic holiday!