What is a good technique to use on data that has many categorical variables with many possible values? For example, let's say you are trying to determine what kind of people are more likely to purchase again from your online store and you have E-mail, Country, Browser. Each variable may have 10+ possible values (e.g. Email: yahoo, gmail, hotmail; Country: USA, Canada, Australia, etc.). Plus you also have continuous variables such as the shoppers age and how much they have spent so far.
I have tried using a logit regression but with so many categorical variables, it gets too big and unwieldy. A multiple regression also has the same problems (too many dummy variables).
A decision tree seems to work best, but it requires turning the continuous variables into categorical variables.
Just wondering what kind of solutions/techniques people have applied to similar situations.
Note: I can use R and other stat software.