How to get new tab/link opened on the right of the current tabs in Chrome web browser?

TabsPlus gives you the option to select where you want a new tab to open - selecting "last" will result in the behaviour you want.

(TabsPlus is not working sometimes)

Try Tab Position Options

Tab Position Options empowers the user to select the tab order. It is possible to select the tab opening position, the new tab behavior and the behavior after closing a tab in the Chrome browser.

Available options

• Activate Tab After Tab Closing
• New Tab background
• Open pop-up window as new tab
• External Links in New Tab

I use Tab Position Customizer 2 for this. When you bring up the options for this extension, the first set of options, titled "Tab Opening Position" allows you to set where new tabs open.

I've tried TabsPlus, which is recommended by the currently accepted answer but found that it does not work with multiple windows.

I've checked Tab Position Options, which was recommended by another answer but I did not like the fact that it required the ability to read and change data on the pages I visit in addition to requiring the ability to read browsing history. Tab Position Customizer 2 only needs the ability to read browsing history (same as TabsPlus).