I love the spring (March - May) Milky Way in the Northern Hemisphere, where the Milky Way rises almost parallel to the horizon of my landscapes. The Milky Way also does that in the spring months (September - November) in the Southern Hemisphere.
I also like the vertical Milky Way we get in the Northern Hemisphere during the summer months (and into September) — it all depends on the composition I'm trying to create with the landscape. My Southern Hemisphere friends get a similar effect during the winter months (June-August), only the core is usually much higher in the sky—sometimes it's directly overhead!
Some photographers like the months where the Milky Way is core is absent, but certain constellations are more prevalent in the night sky (winter for the Northern Hemisphere and summer for the Southern Hemisphere).
Above image taken from my Milky Way NightScapes ebook, pages 15 and 17.
What's Your Favorite Nightscape Season? (You can choose multiple seasons.)