I don't know if someone has already posted something like this, but I'll have a go at it anyway.
I know one can go get a past life regression, but is there another way to find out who you were? Because I feel strange connections that I can't really describe to different parts of history. And I always have dreams that I drown in.
So, could these strange feelings of connections/fascinations and dreams be a sign of a past life? How many past lifes can one person have?
Thanks in advance 
I´ve been researching this for years, well, that means as many years as I´ve been capable of searching. As a toddler its a bit risky wandering into libraries and demanding literature about reincarnation. LOL.
The only clear answer I have found ( and this is just speaking for myself) are the teachings of Daskalos ( The Magus of Strovolos ) and the marvellous works of Buddha, Krishna, and Joshua Emmanuel. Personally I am quite convinced they might be all one and the same person. But lets get back to your question.
If you are having recurring dreams, with the same thing happening over and over, then some psychiatrists would of course refer you to " childhood traumas" etc etc.
But, if you have been quite serious in your personal questioning of your " childhood development " and you can not find an incidence which would suggest a " feeling of drowning " ( sorry, but thats how they work ) then you might be indeed on the right path in thinking that your dreams are reminding your present soul-self about a past life.
How many you can have ? Well, according to Buddhism, you will have as many as you need to become so advanced that you simply dont need to incarnate any longer. The main goal is the attainment of perfection, which means you do not need a body, your Soul-Self will attain the highest Nirvana ( Heaven, Paradise, the Oneness with God )
So, getting beyond this basic lesson " yawn" !! You could indeed seek a serious therapist who could help you into a past life regression. I would be very very careful about this though. You really must find a credible therapist, perhaps someone on the boards here could recommend ???
A life without festivity is like a long journey without rest. ( Demokrit. 460-370 BC ) God didn´t give me a brain just to fill the space between my ears. ( Ayna- ca. 1992 !!! ) I am the seed of all things that are ( Krishna )