What kinds of testing should be considered in the development of software application?

Black box testing: These tests are based on requirements and functionality. These tests are not based on any knowledge of internal design or code.
White box testing: This testing based on knowledge of the internal logic of an application’s code. Tests are based on coverage of code statements, branches, paths, conditions in code.

Unit Testing: Generally Unit testing done by the programmer and not by testers, as it requires detailed knowledge of the internal program design and code. This test particular functions or code modules. Not always easily done unless the application has a well-designed architecture with tight code; may require developing test drive modules or test harnesses.

Incremental integration testing: this testing will be used when new functionality is added; requires that various aspects of an application’s functionality be independent enough to work separately before all parts of the program are completed, or that test drivers be developed as needed; done by programmers or by testers.
Integration testing: Testing of combined parts of an application to determine if they function together correctly. The ‘parts’ can be code modules, individual applications, client and server applications on a network, etc. This type of testing is especially relevant to client/server and distributed systems.

Functional testing: black-box type testing geared to functional requirements of an application; this type of testing should be done by testers. This doesn’t mean that the programmers shouldn’t check that their code works before releasing it (which of course applies to any stage of testing.)

Smoke Testing: typically an initial testing effort to determine if a new software version is performing well enough to accept it for a major testing effort. For example, if the new software is crashing systems every 5 minutes, bogging down systems to a crawl, or corrupting databases, the software may not be in a ‘sane’ enough condition to warrant further testing in its current state.

Regression Testing: Re-testing after fixes or modifications of the software or its environment. It can be difficult to determine how much re-testing is needed, especially near the end of the development cycle. Automated testing tools can be especially useful for this type of testing.

Acceptance Testing: Final testing based on specifications of the end-user or customer, or based on use by end-users/customers over some limited period of time.