Assuming the Requirements of web-based Address book as:
(1)Able to add & delete new  contacts
(2)Able to search/view contacts with sorting functionality

Testscenarios are:
(1)User can successfully add new contact to address book
(2)Duplication of contact is identified.
(3)User can successfully Delete the required Contact.
(4)User can view the contacts from the Alphabetic order 
(5)User can manully search by entering the search criteria.
   from the search menu option.

the above are the sample scenarios if you are good thinker 
then there can be more testscenarios and sub scenarios.

I Continew the 1 answer writen by .....

(1)User can successfully add new contact to address book
(2)Duplication of contact is identified.
(3)User can successfully delete the required Contact.
(4)User can view the contacts from the Alphabetic order 
(5)User can manually search by entering the search 
criteria. From the search menu option.
6) Validate entering the contact (example specific 
characters are compulsory like "@" and ".")
7) If the address book is for specific company then only 
entering email ids with that company's domain is mandatory 
(eg. xyz@softcorner.com is allowed and xyz@gmail.com is not 
allowed)
8) Users that have left the company their email id should 
be popping up some warning msg...After checking form the 
database if it exists
9) IMP: add more than 100 records and see if the variables 
used accept more than 100 users....sometimes using default 
data types gives this error
10) They should preferable use the best search algorithm 
instead of tradional one for faster search as that is very 
imp in searches...
The above are the sample scenarios if you are good thinker 
then there can be more test scenarios and sub scenarios.

11) Last one which i think is imp: the search should be as 
appropriate as possible with accurate results

Assuming the Requirements of web-based Address book as:
(1)Able to add & delete new  contacts
(2)Able to search/view contacts with sorting functionality

Testscenarios are:
(1)User can successfully add new contact to address book
(2)Duplication of contact is identified.
(3)User can successfully Delete the required Contact.
(4)User can view the contacts from the Alphabetic order 
(5)User can manully search by entering the search criteria.
   from the search menu option.

6) the above are the sample scenarios if you are good 
thinker 
then there can be more testscenarios and sub scenarios.
IMP: add more than 100 records and see if the variables 
used accept more than 100 users....sometimes using default 
data types gives this error
7)Last one which i think is imp: the search should be as 
appropriate as possible with accurate results