I dunno, stuff I like to see are when they really look they lost their senses? How to put it? Small details I like is like when the stumble a lot, struggle to keep balance or bend their legs like Cammy does in that vid of SFV, when they look up or have their arms hanging. The expressions also help a lot, perhaps that's why I like Samus's dizzy so much in SSB4 she has a very nice expression of dizziness. Guess that's what makes Super Street Fighter II Cammy's dizzy my favorite: she stands there groggily without the same pain expression of the Alpha series, she looks like she lost her senses.
One thing that really brings the whole thing down though is when they put their hands on their head or their body (like their stomach or chest), I dunno why but it really bothers me. I can let it pass when all the animations in the game are similar or low key, but more oftern than not it really sticks out. This is probably why I have such mixed feelings with Palutena's animation in SSB4, everything is perfect except for her hand and given how many dizzies are in that game it bugs me a lot... Dunno why, really. THough her expression, really really helps. Talking about expressions, if it is boring it also kind of bothers me, but this is only if the game has dizzy expressions, if all the animations have a pain expression or just eyes closed (like in Tales games) I don't mind, but again like in SSB if there are expressions around, which that game has aplenty, having a boring one undermines things... which is what happens with Zelda for me (I love her animation overall), she is my favorite Nintendo girl and her dizzy was so close to perfection but her having the same expression when she gets hit really made me feel "Aww... really it was almost there almost perfect!" I really wish she puts the same face as Samus or Peach when stunned.
On another weird note, having a dizzy "effect" also helps things up, having the circling birds or stars on the character's head is what completes the thing for me. When it isn't an effect, it doesn't bother me like the things above, but it does become much less appealing. This is epecially nice if there is a sound effect like tweeting or something accompanying things. You may guess how excited I was when I found out that SSB4 had added a circling stars effect to stuns.
