Well, it is wrong to assume that just because you don't believe in the legitimate existence of a state or morality as a state-enforcable concept, it is ok to act like a beligerrent asshole and hurt other people. Stealing from a bank usually hurts the people who have their money in the bank more than the bank itself (duh, that's how capitalism works, profit moves up, cost moves down), and it really just makes you a slightly unconventional capitalist. That being said, some illegalist activity, such as counterfeiting money and smuggling was more productive.
However, pissing off capitalists with petty, superficial crime is really just a fruitless cause. In a war of crime and/or violence against the state, anarchists will nearly always lose because, unless they have the vast majority of the country on their side, they don't have the authority or the structure to retaliate effectively. Thinking that you can undermine the state through crime is like trying to dig a hole to China, one spoonful at a time, except with the state retaliating the whole time with bulldozers.
The only war that anarchists really have a chance of winning, at least initially, is a war of ideas, supported by a dissatisfied proletariat (or whatever else you want to call the group of people not profiting from capitalism). Illegalism is greatly damaging to this war, because the state-run media is more than happy to use it as propaganda, and it really hurts anarchism's legitimacy in the public eye. Marx learned this in Germany when he alienated the workers with his violent Communist propaganda (hence the reason why the "social democrat" movement of the 1860's was very careful not to associate itself with Communism), which resulted in his Communist Manifesto not really reaching a major audience until it's resurrection by the Leninists, a generation later.
Illegalism, along with an extremist American reaction to anything associated with Marx and Communism, is what has caused anarchism as a viable political theory to fall from grace in the public eye and attain the terrible reputation and stereotypes associated with it today. The majority of "illegalists" today are naive teenagers who shoplifted their bright colored Mohawk dye and "punk music" cds from Wal-Mart and think anarchism is all about skipping school, staying up past curfew and scaring their parents.
I would argue that a much better alternative strategy to illegalism would be non-participationism, in which you try to separate yourself from the state and the capitalist system as much as possible in your own lifestyle. In that way, you can become a positive example rather than a negative threat. People remember Ghandi in a much better light than they do Sacco and Vanzetti, and I would argue that he got a lot more done.