Wave petunias definitely bloom more and for a longer time than regular petunias when not deadheaded. Geraniums usually keep going all summer without attention.

If you hate deadheading, maybe some foliage plants like coleus, caladiums, or the trailing tradescantias would be enjoyable. The leaves look pretty all the time, no flowers needed.

I've never been able to grow geraniums without regular dead heading and even stopped using them years ago. Perhaps it's time for me to look into them again, if they no longer need such attention. Of course, my attempts were in the south, and summers here can be trying on geraniums.

My favorite carefree annual would be the Profusion zinnias, with the little angustifoia zinnias a close second. I'm also a fan of portulaca. All three laugh at the summer heat and sun and never need to be deadheaded.

Hopefully, others will chime in with their favorite carefree annuals, too.

Calibrachoa (Million Bells) are like mini petunias and do not require anything but water and sunlight. I like them so much better than petunias.

Here is a link that might be useful: Million Bells

Disagree re: annual geraniums. They definitely flower more when deadheaded. I don't grow Wave petunias, but the regular petunias will peter out mid-summer unless sheared back/deadheaded.