I have City points and a Country polygons. Is it possible to make it so that labels of the cities are inside of their own country without converting to annotation?
I'm using ArcGIS 10.1 for Desktop.
Arc 10.1 gives you access to the Maplex Labeling Engine which is pretty powerful and should allow you to automatically place your labels.
There is a wide range of options for you to tweak and adjust but I would recommend starting with the point placement options and then look at the weighting:
In the placement properties you can give the city labels various parameters - take a look at all the tabs and have a play around. But ideally you want to let the engine figure out the best place automatically.
In order to ensure the labels stay within the polygons you can adjust the weighting or 'importance' of the labels and poylygons. A brief description is given at the bottom of the first link above, but basically the weight ranking button (third one in the tool bar above) allows you to say which feature or label is more important by giving them a ranking.
Again have a play around with the numbers and see how it affects the positioning of the labels but it should be possible to find a combination of settings that will keep the city labels inside your country boundaries.