Most common types of audit services include:

External audit (statutory audit)
These are the most widely used audit services. Examination of the accuracy of the financial statements is entrusted to external and independent auditor, who cannot be connected to the company or have any interest in the outcome of audit (no conflict of interests). The annual financial statement is certainly the main resource of accountability of the company. Since the financial statement is prepared and approved by the board of the directors, the shareholders of the company would rely on the external way to verify the report. Therefore, they invite external auditors. Moreover, regulations of many countries prescribe to run statutory audit on annual basis;
Internal audit (operational audit)
This is a voluntary pocedure of the organisation, willing to examine the effectiveness of inner control, verify and monitor possible fraud, check financial data, examine operational process and other activities. Basically, any company may conduct it for its own sake;
Tax audit
Tax audits are performed by tax authorities within regular intervals in some jurisdictions or in other randomly chosen countries. The purpose of the tax audit is to check company’s tax liabilities and to analyse accuracy of the filed tax returns;
Forensic audit
This is a special investigational audit conducted by legal officers and is often used in courts and investigation processes in order to determine frauds, tax evasion cases, money laundering and other illiegal actions within the framework of the company or its responsible officers.