Because this is a shipping thread, I guess I will tell you all my beliefs. I believe that Ash (Satoshi) and May (Haruka) will probably end up together. At least, I think they should.
Although there are a good many people out there who believe otherwise, and re so entitled to their opinions. If we look at each girl that Ash (Satoshi) has traveled with, we can easily see a different relationship with each one. Each girl brought out something different in him.
Let's start with Misty (Kasumi), shall we. The whole reason for her joining Ash on his journey was because he owed her a new bike. However, along the road to the indigo league we see that she grows to have more of a friendship with Ash and eventually forgives him for the bike. In the entire first season (Indigo League) we do not see anywhere that she shows favor in any other way than a good friendship might. In fact, the only instance that I know of where misty shows real dedication to ash isn't until the Orange League battle with Rudy (Jiji) on Trovita Island. However, most people (and Rudy) took her defense and rooting for Ash over Rudy to mean that she wanted to be more than friends. I however believe otherwise. I believe that she had been traveling with Ash for so long that the friendship between her and Ash had grown to be more of a sibling type relationship. When she and Ash began traveling she began to be his mentor of sorts. She knew much more about Pokèmon than ash did, so he looked up to her, Sort of as a little brother might look up to a wiser older sister. I therefore conclude that any sort of future relationship with her will be purely friendship.
After Misty decided it was time for her to return to the Cerulean gym, they introduced the new region of Hoenn and May (Haruka). We could all see that may liked Ash right off, in the first episode (when Pikachu has too much electricity build up). At the end of that episode we get a clear hint that she likes Ash buy the way she gets him to travel with her to Petalburg. The way that Ash and May acted around each other, anyone could tell that they kind of liked each other, but as younger kids do, they would never admit it out loud.
To this day I'm not really sure why May decided to go to Johto without thinking about Sinnoh.
That leads us to the current episodes, and also back to the mentor/student relationship. However, this time the roles are reversed. This time Ash is the mentor and Dawn (Hikari) is the student. With it being so early in the season, I can't say what future episodes might hint at, but for the time being, I believe that Dawn thinks of Ash as her friend/ mentor and probably isn't thinking of anything, well, romantic at the moment.