Can other people see my wantlist?

By default, no — your wantlist is private. There's no public wantlist page, and other collectors can't browse what you're hunting for.

The one exception: shows

The only time you share wants is when you choose to. At a train show you can share specific wantlist items with that show's registered attendees so they can spot them for you on the floor. You pick which items to share, and it only applies to that show — see How do I share my wantlist at a show?.

Everything you don't explicitly share at a show stays private to you.

See also What is the wantlist?