3D: the Dead or Alive series, particularly 2U and 3 come to mind (I didn't spend enough time with 5 or 6, but they probably count too).
It's built upon Vitua Fighter framework, but feels a little easier and more newcomer friendly. The counter mechanism is kinda rubbish, but that has little to do with "feel" of the gameplay. The characters, pretty much all of them, feel good to play.
2D: I'll need to think about this for a while, but when talking about games that are easy to get into on a first try... Melty Blood.
Something about it just clicks. I'm not a huge fan of the character designs, but the gameplay just feels great. I wish they'd port it to consoles, since my PC doesn't like to let me stream it properly for whatever reason, so I barely play it.