It is possible to make ice cream without an ice cream maker, but your ice cream will likely not be quite as smooth or creamy. By stirring the freezing mixture regularly, though, you can keep the ice crystals to a minimum.
My friend David Lebovitz ,the renowned pastry chef who has written an entire wonderful book on ice cream called The Perfect Scoop (yes, I choose my friends well!) has a great post on his blog that explains the method for making ice cream without a machine. I believe his method would work with many other custard-based ice cream recipes.
For some top-rated ice cream recipes, see Summer's Best Homemade Ice Cream.