I performed Installation testing, browser compatability 
testing, regression testing, parallel testing.

Testers can perform Balck box testing,Grey box 
testing,Smoke testing,Sanity testing,endurance 
testing,automation testing,volume testing,Database 
testing,Stress testing,End-end testing,alpha testing,adhoc 
testing,concurrency testing ....List will not end!!!!!!!

Tester can perform Black box testing,GUI testing,DataBase 
testing,Integration(Tester+Developer)System and UAT.As per 
Client requirements.

Moreover testers perform sanity testing, black box,
regression, performance, volume, system testing and installtion.

I would like to add something here

Black Box & White box testing are two approaches of testing
Most commonly every tester perform
1.Functional testing
2.Regression testing
3.Re-testing
4.Sanity testing
5.Compatibility testing
6.UI testing
7.Exploratory tesing (this is depending upon the type of 
project)
8.end to end testing
9.adhoc testing
10.Installation testing

I would tell that  System testing,because  all testings are 
covered in System Testing.

Kinds of testing means:

1. Static testing      &  Dynamic testing.
2. Structural testing  &  Functional testing.
3. Automation testing  &  Manual testing. 

Testers  will do only:

Dynamic    testing
Functional testing
Manual     testing

functional testing,regression testing,database 
testing,integration testing,compatability testing,security 
testing,cookie testing,alfa testing,beta testing,etc..

I think,only Naren's Answer is right.
Asked question is not about to List out available Kinds of 
Testing,but which Test U have done in your organization

These are the possible kind of testings a tester can able to
do in his/her testing phase.

Mainly System Testing in that only all will come like
1)Functional Testing in that
  a)Sanity Testing
  b)Black Box Testing
  c)Manual Testing/Automation Testing
  d)Static Testing
  e)Dynamic Testing

2)Non functional Testing in that
  a)Usability Testing
  b)Alpha Testing
  c)Beta Testing

3)performance Testing in that
  a)Stress Testing
  b)Load Testing
  c)Endurance Testing

Regards
Preethi.G