You have three main choices:

1. Use an Iterator, since it has that handy remove method on it. :-)

   Iterator<String> it = list.iterator();
   while (it.hasNext()) {
       if (/*...you want to remove `it.next()`...*/) {
           it.remove();
       }
   }
   

2. Loop backward through the list, so that if you remove something, it doesn't matter for the next iteration. This also has the advantage of only calling list.size() once.

   for (int index = list.size() - 1; index >= 0; --index) {
       // ...check and optionally remove here...
   }
   

3. Use a while loop instead, and only increment the index variable if you don't remove the item.

   int index = 0;
   while (index < list.size()) {
       if (/*...you want to remove the item...*/) {
           list.removeAt(index);
       } else {
           // Not removing, move to the next
           ++index;
       }
   }
   

Remember that unless you know you're dealing with an ArrayList, the cost of List#get(int) may be high (it may be a traversal). But if you know you're dealing with ArrayList (or similar), then...