An overstay leaves a mark that outlasts the trip. Most immigration systems record it against your passport details, and future applications commonly include a direct question about past overstays anywhere in the world, not just in that country. Answering dishonestly is usually a worse offense than the overstay itself, since misrepresentation can bring long or permanent bans.
The practical impact scales with the length. A day or two, promptly explained, is often forgiven or handled with a small fine. Weeks or months can trigger automatic re-entry bans of one to ten years depending on the country's rules, and visa officers everywhere read a substantial overstay as a red flag for compliance.
If you have an overstay in your history, your best tools are documentation and honesty: keep evidence of the reason, such as medical records or airline cancellations, disclose it when asked, and address it head-on in a cover letter. For significant cases, a consultation with an immigration lawyer before the next application is money well spent.