The best replacement for jquery ajax is xmlhttprequest.

The best alternatives to jquery ajax are rated as following:
★★★★★  xmlhttprequest
★★★★  asp.net ajax
★★  javascript ajax
★  asp net
★  updatepanel

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Speaking about jquery ajax, one probably shouldn't forget about parameters.

Other search terms related to jquery ajax and their ratings are:
★★★★★ parameters
cors
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jquery ajax
xmlhttprequest
asp.net ajax