Here sample for Opportunity:
1. Create a formula field in Opportunity
- Do not need to add the field to any page layout, but make it visible to Profiles as required
- Set Formula Return Type = Text
- Type Label = Action
- Formula = HYPERLINK('006/e?id='&Id, 'Edit' , '_blank'), this formula will open new tab in the web browser when user click Edit link in report, or change _blank to _self if you prefer user to open the record in the same tab, meaning it will close the report.
2. Create Opportunity report
- Select Tabular format report
- Drag fields needed to the report and add the filters as normal report
- Drag Action field from field list, preferably at the most left.
Note: if you need to have Action field for each object in the report, you need to create the formula field for that object.