Next, is when Ash lectures May, telling her that she should go on ahead to Pacifidlog, while he takes care of Max. That really showed me that he cares not only for to realize her dream of becoming a Top Coordinator, but that he also cares about the well-being of the people that mean a lot to her (her brother, no less). Her reaction (crying, then immediately wiping away her tears in an effort to not look weak, then sincerely thanking him) was also really shippy, in my opinion.
A close second is when May "follows" Ash all the way to Pallet, just to be able to travel with him again (AG 133). I dunno, just the fact that she went through the trouble of going to Kanto, finding out where he lives and showing the desire to stay by his side before even finding out that Kanto also hosts contests is pretty awesome. I also like how Ash was first to invite May to travel with him, when it's usually the other way around.
I also think that when May and Ash pull out their respective halves of the Terracotta ribbon, then proceed to put it back together and re-affirm it's importance to them (May in particular) is gold. The fact that they both have it on-hand (Ash doesn't have his bag on him, implying that he keeps it on his person) is also awesome. Then there's the sentimental departure at the end of DP 077, with May holding her hand over her heart while talking to Ash, of course.
Then there's also the episode where May is trapped in the jungle reserve-thing and Ash goes against everyone and goes out of his way to save lil' old May.
Of course, Movie 9 is also up there, for blatantly obvious reasons.
So there you have it. My favorite Advanceshipping moments of all-time. I actually took the time to re-watch each individual episode that I've mentioned, just to make sure that the facts are straight. That's the most work I've ever put into a post.
I'd like to say that at the current time, I'm at episode 168 (of 192) of the Advanced Generation Saga, so more shippy moments are sure to come. I can't wait for the famous "ribbon episode".
Also, to clarify, though I haven't seen the ribbon episode yet, I decided a while back to watch the 3 episodes in DP that have May in them. I did that because I'm not sure if I'm gonna watch the DP saga and I wanted to see May in all her glory. She is my favorite female companion, after all.
God I love this ship
Okay, so I expanded on this way more than I originally intended to. Oh well, it can't be helped. Bang. Wall of text, for your enjoyment.