How well should features discriminate to build a good classifier from them? For my (binary) classification problem I'm developing several features and tune them with ROC curves. 
At some point, I want to combine them with in classifier.
How well should the features perform, for example in terms of AUC,  to discriminate my data "good enough" and build a powerful classifier out of them?
This is a very general question, but maybe you know interesting literature on that.
 A: Your question starts from a wrong premise, being that the performance of a classifier is always directly contingent on the performance of individual features. It is perfectly possible to build very good models based on (individually) bad features.
Consider a double helix, with features $x_1$, $x_2$ and $x_3$, as depicted in the figure. Lets say the helix is aligned with one of the features.

If we only look at any feature individually it is impossible to make a good classifier (the AUC per feature would be 0.5). The same even holds for any pair of features. However, given all 3 features it's possible to build a perfect model.
So in short: there's no rule-of-thumb for minimal performance per feature for it to be useful.
A: You could use a backward feature selection algorithm: provide all possible features to your classifier, assess its performance (for instance with the auroc you mentioned). Then remove the features one by one and each time assess the performance of your classifier and the p-value between your previous classifier (or the initial one) and the current one. When the p-value is significant, you stop removing features, this is your best model.
To assess which feature to remove, you can have a look at the feature importance if you use a random forest classifier or the features weight if you use a logistic regression.
