We worked for months on it, and now it is available: Make searchable PDFs from scans and images for free with our Online OCR form and the OCR API.
This works with PDFs with images inside (such as the ones you get from scanning documents) but also works with images (jpeg/png/gif). The image is converted to a searchable PDF that you can download.
Try it here and select the “Create visible text layer” option. This way you can easily see the text layer that gets added during the conversion.