I've got a pretty old bathroom, and there are some rust-alike stains along the tiles seams. I guess this is normal in wet environments? Scrubbing off doesn't really help. What is usual way to fix it? Of course, I would not want to rip off tiles and install new, may be just putting some caulk would be sufficient?
There's a good cleaning solution for this called CLR (US) - it stands for Calcium-Lime-Rust. This will dissolve rust and hard water spots in showers, if you do indeed have rust.
You mentioned scrubbing doesn't help, if you haven't tried CLR I would do that next. Otherwise, you're probably looking at re-grouting.
It is possible to caulk these seams and that may work, but they're intended to be grouted. Caulk is not a good permanent solution here. Grout can be removed with a cutting/grinding tool, and it's relatively easy to apply. Color matching the existing grout may be difficult