If you go to your bookmark manager, it might have something that says “Export” on it. You can then export all your favorites to a document on your computer.
When you want to import them to a new browser like Chrome or Firefox, go to the browser’s bookmark manager and click import, and then choose the file with your bookmarks you exported and import them.
Or you could use Google Bookmarks, and you wouldn’t have to transport bookmarks again. Google Bookmarks works along the same lines. You import your bookmarks from the file you exported.