For recent press releases, see PR Newswire, or Business Wire and several foreign wire services. You might also want to search Google for the relevant company, agency, office, organization, etc. and/or check the website of the company/agency/office/organization/etc. Westlaw's WIRES database has about 18 newswires going back 90 days.
For older material, Bloomberg Law has a substantial collection of newswires, including US Federal Newswire, PR Newswire and Business Wire. Westlaw's WIREPLUS database has about 18 newswires.
Canada: Canadian press releases are available from Canada Newswire and Industry Canada Online. Bloomberg has Canada Press back to 2008.