You're mixing up declarations and instantiations.  When you declare a template, you don't specify a type immediately after its name.  Instead, declare it like this:
template<class T>
class Node {
private:
  const T x_;
  Node *next_;
public:
  Node (const T& k, Node *next) : x_(k), next_(next) { }
  const T& data(){return x_;}
  Node *get_next(){return next_;}
};
Your original declaration also confuses string, const char *, and generic types that should be in terms of T.  For a template like this, you probably want to let the user define the type of the member (x_).  If you explicitly declare it as const char * or string, you're losing genericity by limiting what the user can use for T.
Notice that I changed the types of the instance variables, the parameters of the constructor and the return type of data() to be in terms of T, too.
When you actually instantiate a variable of the template type, you can provide a concrete type parameter, e.g.:
int main(int argc, const char **argv) {
    Node<char*> *tail = new Node<char*>("tail", NULL);
    Node<char*> *node = new Node<char*>("node", tail);
    // do stuff to mynode and mytail
}
Whenever you write the template name Node outside the template declaration, it's not complete until you provide a value for the parameter T.  If you just say Node, the compiler won't know what kind of node you wanted.
The above is a little verbose, so you might also simplify it with a typedef when you actually use it:
typedef Node<char*> StringNode;
int main(int argc, const char **argv) {
    StringNode *tail = new StringNode("tail", NULL);
    StringNode *node = new StringNode("node", tail);
    // do stuff to mynode and mytail
}
Now you've built a linked list of two nodes.  You can print out all the values in the list with something like this:
for (StringNode *n = node; n; n = n->get_next()) {
    cout << n->data() << endl;
}
If all goes well, this will print out:
node
tail