A radical can be neutral, positive or negatively charged.
If an anion is oxidised (loss of an electron) you get a neutral radical. So for example the phenoxide ion can be oxidised by Fe3+ to give the neutral phenyl oxygen radical while Fe3+ is reduced to Fe2+. Also if a neutral molecule is split (called homolytic bond fission), for example Br2 going to two Br. radicals, you get neutral radicals. Neutral radicals are the most common in solution.
You can get radical anions and radical cations by adding or removing (respectively) a single electron from a neutral species. This behaviour is most commonly seen in the gas phase, for example in mass spectroscopy.