It is important to understand that data sharing is an expected part of every data management plan requirement.
There are a few cases when data sharing may not be appropriate. In general data which may compromise research subjects or be tied to intellectual property such as patents, are acceptable exceptions.
In select circumstances it may be acceptable to not share your research data. These reasons may include research subject privacy or protection concerns or intellectual property rights such as pending patents. If your research falls into one of these categories make sure to articulate why publicly sharing the research data would be detrimental or illegal. It may be possible to simply limit access to the data, or to apply usage requirements as a compromise.
Different agencies have different requirements on when research data should be made available. Some agencies require that the data be made available at the time of publication while others simply require the data to be available within 12 months or within a "reasonable time" after publication. Make sure to check the exact requirements of the sponsor as they may have a specific time period that you need to comply with.
A statement that "data is available upon request" does not show a strong commitment to data sharing. Because of this it's a good idea to share research data in a more formal matter, in effect "publishing" the data. Sharing data in a formal way also provides some additional benefits such as:
Not all data publishing venues are created equal. A common way to "publish" data is to publish data as journal article supplementary information (SI) file. While this is an easy way to share data, not all SI files are publicly available, assigned a DOI, or assigned metadata different from that of the article (which will make it more difficult to find and track). Make sure share your data via a method that satisfies all requirements and fits your needs.
If there is an acceptable reasons to restrict access to your research data then make sure that the method of data sharing you have chosen is compatible with your restriction needs. Keep in mind that many data repositories require you to apply a CC0 license to your datasets which is not compatible with usage restrictions.
Making data accessible is only one-half of data sharing. The other half is making sure your data has enough documentation for it to be meaningful and useful to others. Some repositories will not accept your data unless it is accompanied with a readme file, data dictionary, or other forms of metadata or documentation. See section 3: Data Documentation for more details.