I will cover some major negative test cases to break the sign up page:
1) See the limit of username field. I mean the data type of this field in DB and the field size. Try adding more characters to this field than the field size limit. See how application respond to this.
2) Repeat above case for number fields. Insert number beyond the field storage capacity. This is typically a boundary test.
3) For username field try adding numbers and special characters in various combinations. (Characters like !@#$%^&*()_+}{“:?><,./;’[]). If not allowed specific message should be displayed to the user.
4) Try above special character combination for all the input fields on your sign up page having some validations. Like Email address field, URL field validations etc.
5) Many applications crash for the input field containing ‘ (single quote) and ” (double quote) examples field like: “Vijay’s web”. Try it in all the input fields one by one.
6) Try adding only numbers to input fields having validation to enter only characters and vice versa.
7) If URL validation is there then see different rules for url validation and add urls not fitting to the rules to observe the system behavior.
Example urls like: vijay.com/?q=vijay’s!@#$%^&*()_+}{“:?><,./;’[]web_page
Also add urls containing http:// and https:// while inserting into url input box.
8 ) If your sign up page is of some steps like step 1 step 2 etc. then try changing parameter values directly into browser address bar. Many times urls are formatted with some parameters to maintain proper user steps. Try altering all those parameters directly without doing anything actually on the sign up page.
9) Do some monkey testing manually or automating (i.e. Insert whatever comes in mind or random typing over keyboard) you will come up with some observations.
10) See if any page is showing JavaScript error either at the browser left bottom corner or enable the browser settings to display popup message to any JavaScript error.
These are all the negative test cases. I assume that you already tested the same sign up page with all valid cases to check application is working fine as per requirements.
If above cases are not breaking the application page then don’t forget to praise the developer ;-)
If you have some killer test cases to break such applications that you learned from your experience, you can specify them in comments below.