The best replacement for wire nut is electrical tape.

The best alternatives to wire nut are rated as following:
★★★★★  electrical tape
★★★  crimp
★★★  solder

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Speaking about wire nut, one probably shouldn't forget about pigtail.

Other search terms related to wire nut and their ratings are:
★★★★★ pigtail
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wire nut
electrical tape
crimp