I have learned that resampling e.g. bootstrapping could give us better results for some problems. If we have a huge data set (millions of values) does it make sense to do some kind of resampling or these methods are only suitable when the data set is not that big?
There is no reason why bootstrapping would be inappropriate with a large dataset, if inappropriate means deliver bad results because of the size. However, depending on how large the dataset and how complex the calculations that need to be done, there might be cost or efficiency problems.
Since you have a huge dataset, you have the ability to validate many ideas on totally clean data. Keep a large portion at the side and go and try many ideas. You have a great "sit belt" that will prevent you from huge mistakes without having to worry about the dependencies of cross validation, overuse of specific samples and so. You are risking time, not performance.
As for the specific question of bootstrapping. Bootstrapping is usually used in order to reduce the variance of the model. You have a large dataset so the variance of the DATA should be low. However, it is possible that you use a classifier that its variance will be high so bootstrapping will help you. neural nets, classication and regression trees, and subset selection in linear regression are considered unstable (here , as self reference of Leo Breiman in Bagging Predictors)
Also, in many cases the dimensionality of the data is extremely high and your dataset doesn't cover it well enough.
When your dataset is imbalanced many classifiers might give you a prediction that is quite similar to the majority rule. Using bootstrapping might help but in such cases I would recommend using technique like boosting that deliberately forces the learner to focus at areas of interest.
Another benefit of bootstrapping is getting a confidence level for the prediction. However, since most classifier provide confidence this is usually not the reason to use bootstrapping.