It is possible to make ice-cream without an ice-cream maker, but it is not recommended as it is time-consuming and the result will not be as smooth nor the volume as great. This judgement does not apply to ice-cream parfait, which uses a different technique.
You really need an ice-cream maker which, used in conjunction with a food processor or blender, makes it possible to produce a range of perfect ices and sorbets effortlessly. An ice-cream maker is an expensive piece of kit and several of the larger ones need to sit untouched for 24 hours before use because of complex balancing mechanisms. This means that you need space in the kitchen to keep them on a work surface permanently.