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Chrome for iOS - Free
I'm increasingly replacing Safari with Chrome (free, App Store) on my iPhone and iPad. Chrome has a modern UI with a unified search/URL field, unlimited tabs that you can flip through like a deck of cards and synchronization of tabs, bookmarks, passwords and omnibox data across devices that actually works. Mobile Safari on the other hand, feels like a relic of days gone by. It requires an extra touch to search, limits you to eight "pages" (no tabs), and iCloud bookmark syncing that is so broken that I leave it turned off.