If you're interested in commercial aviation (ie. a career) then this is useless babble, but otherwise you've got tons of non-medical options: Part 103 aircraft, balloons, gliders and perhaps light sport.
A quick note on medicals as relates to the ballooning world. It used to be that no one (student, private, commercial) required a medical... things are changing due to the idiotic balloonist in TX that killed over a dozen passengers in 2016. Interestingly enough, it's not as much the NTSB or FAA that is mandating changes (though they probably will at some point in the coming future), it's the insurance companies (of which there are only a few who cover ballooning operations). My agency came out with a memo last year that starting in 2018, commercial pilots will require a second class medical and ALL pilots flying a balloon of 140,000 cubic feet or greater (6-10 passenger and above) will need at least a third class medical regardless of commercial ops or not. This is a rare example of literally one person's F-up changing an entire industry. The FAA knows little about ballooning so the BFA (Balloon Federation of America) jumped on them and the NTSB to 'work together' before stuff gets too out-of-hand, regulatory speaking.
