My human subjects research is "exempt" under US regulations. Does that mean I can skip ethics review?
Regulation
No, you cannot skip all the process.  The word &quot;exempt&quot; is misleading.  The exemption is from most regulatory requirements, not institutional or journal requirements.  Exemption is specific to the regulations of the United States.
Regulations do not require IRB review of exempt research.  Regulations do require determination.  Depending on your institution's policy, the determination might not be conducted by the IRB.  But usually it is.  If your institution permits it (which is highly unlikely), you may be able to conduct the determination yourself.

The regulations do not specify who at an institution may determine that research is exempt under 45 CFR 46.101(b). However, OHRP recommends that, because of the potential for conflict of interest, investigators not be given the authority to make an independent determination that human subjects research is exempt.
The regulations do not require that someone other than the investigator be involved in making a determination that a research study is exempt. What they do require is that there be accurate determinations so that non-exempt research ends up being reviewed by an IRB. Because of the potential for conflict of interest in this situation, OHRP's long-standing recommendation is that investigators not be given the authority to make an independent determination that human subjects research is exempt.

Source
Note that ethics processes which are permitted under United States regulation may be a crime in other countries.
Journal Policy
Furthermore, reputable journals require IRB approval for publication.  The Helsinki Declaration §23 says,

The research protocol must be submitted for consideration, comment, guidance and approval to the concerned research ethics committee before the study begins.

While the Helsinki Declaration is specific to medical research, journal policies typically apply the same requirement to non-medical, human subjects research.  For example, Nature and Science.
How do I avoid the process?
You can avoid the process if you are not doing research or if you do not involve human subjects.