All answers to this question are speculative since we do not know exactly what we would be like today with a different system. We can only judge by comparing our 2 party system to different governments.
I will simply point out that our 2 party system reinforces that radical concept of a "loyal opposition." In other words, you can be loyal to the government while opposing its policies. This is a concept that dictators have a tough time wrapping their minds around. After all, our government it that which was created by the Constitution, while our government's policies are those implemented by simple persons in positions of power. There is a basic difference there.
The existence of a loyal opposition is absolutely essential to our concepts of democracy. In this light I would personally say it has done more good than bad.
It also enables us, the voters, to stage a bloodless revolution every two years (Congressional elections) where we can kick out our leaders and replace them with someone else, instead of having to go to the streets with rifles to do so. Pretty amazing system.
I am going to go with the idea that the two party system has helped more than it has hurt.
I would argue that having a two party system decreases the amount of fanaticism that you will have in a political system. We have a terrible amount of partisanship as it is, but I think it would be worse with more parties. In our current system, the parties generally have to appeal to the middle (at least in presidential elections). Small parties could get away with just playing to their bases (as our parties do in primaries or in places where they hold safe seats).
What the two party system in America has done is given the country stability. America has two broad choices from which to take its leaders. This makes creating and implementing policy much easier than in the European parliamentary system. In that system, you can have two to three dozen different parties vying for power. They then have to form coalitions to make a government. Everyone has to compromise just to get the government moving and are less likely to get their specific policies implemented.
The 2 party system in America has done more damage than has helped this country. The reason is most politicians are not really true to their party system anyway. There are more variations to being republic and democratic. We do not have a 'true' two party system and that has hurt the country. We have liberal democrats and liberal republicans, conservative democrats and conservative republicans, moderates and extremists...the variations and lists go on. During the early days of this country we had even more parties like the Whigs and Federalists. Now with the Green Party, Liberalist Party and so on , I think it is time for people to have more than one definition of their political beliefs but come to a consensus more rapidily and intelligently instead of all the political infighting and grandstanding which has really hurt our country.
I really can't take a side. I believe that has both hurt and help our country.
It has helped because of what has already been said. It has helped broaden the choices that we have when it comes time to choosing our leaders. We are now able to look at the issues that are most important to us and vote based on the issues.
On the other hand, I believe that it has also hurt the country. It has forced us to choose a side and I believe that has torn our country apart to a degree. It has already happened in our national government, when one party gets the majority then it's going to get its views passed. Essentially that will force one party's views on the country when the parties should be working together to do what's best for the country.