Chrome

• Click the Chrome menu Chrome menu on the browser toolbar.
• Select Bookmarks.
• Select Always show bookmarks bar.

You can also use the keyboard shortcuts Ctrl+Shift+B (Windows and Chrome OS) and ⌘-Shift-B (Mac) to toggle the bar on and off.

Safari

• Make sure your Bookmarks Bar is showing
• If it isn't, select View --> Show Favorites Bar
• Now you can drag the button to your Bookmarks Bar

FireFox

Make sure that toolbars like the "Navigation Toolbar" and the "Bookmarks Toolbar" are visible.

• Firefox menu button > Options
• View > Toolbars (press F10 to display the menu bar)
• Right-click empty toolbar area
• Use Customize to open the Customize window and set which toolbar items to display.

• check that "Bookmarks Toolbar items" is on the Bookmarks Toolbar
• if "Bookmarks Toolbar items" is not on the Bookmarks Toolbar then drag it back from the toolbar palette into the Customize window to the Bookmarks Toolbar
• if missing items are in the toolbar palette then drag them back from the Customize window on the toolbar
• if you do not see an item on a toolbar and in the toolbar palette then click the "Restore Default Set" button to restore the default toolbar setup
• How to customize the Toolbar
• Toolbar items are missing

Internet Explorer

Here's a pointer to an article on the Bookmarks bar in various versions of IE.
IE Favorites

Safari on an iPad 2

• Tap on Settings > Safari.
• Toggle Always Show Bookmarks Bar to On.
• Open the Safari browser.
• Tap the arrow icon to the right of the address bar when you want to create a bookmark that will show in the Bookmarks Bar .
• Tap Add Bookmark. Select Bookmarks at the bottom of the box.
• On the next screen you’ll see two choices: Bookmarks and Bookmarks Bar. Tap Bookmarks Bar.