smoke or sanity testing is the first test, where we check
the from login to logout all the functionalities are
testable are not. in some companies the smoke is done
firstand sanity at the end of all tests vice versa
then the functional testing all the things as in the web
application we get the top of the screen we get some
functions , left pane we get some functionalities, right
pane some functionalities, center and bottom from login to
log out. with out missing any thing or any functionalities.
then we apply the regression testing technique for the same
things after fixing the bugs.
then integration testing has to be done checking the
integration of the 
after getting satisfied with the build to the functional
spec requirements. 
then we have to check the performance
last the uat (user acceptance test)
if you need more detail please contact me on my mail
jagadishk.9454@gmail.com 
this varies with company to company

Web Application test includes following tests
1) functionality - sanity, smoke, functionality
2) UI based testing - GUI testing
3)Performace - Load, Stress, Volume
4) Security - Penetration  & security ( acess, 
authorisation & encryption/decryption)

the security testing is needed only for the secured sites
like banking finance etc not for all 
the answer is correct by swathi except the security testing
there is one more testing that is compatibility i.e.
platform independence as this is for web related testing.