In addition to soap or alcohol (my tools of first resort) I have used imidacloprid as a preventive treatment. It's not going to be enough to get rid of an active infestation but it does work to deter new ones. Imidacloprid is an excellent treatment for root mealies in particular.
Speaking from personal experience, there tends to be a human component responsible for mealy bug problems. Or to put it the other way around, vigilance is probably the greatest tool in your arsenal. It's way way easier to deal with bugs when you catch them early. A severe bug problem may reflect errors in cultivation, as Will has mentioned. But it may also reflect a lack of attention.
This human component is particularly important in the resolution of mealy problems. There is no "hit once and forget" solution to these bugs... you have to follow up after the first or second or whatever treatment (twice a week with soapy water) until you see the problem resolved. You have to inspect carefully and double check even after you think the problem is solved.
