-_-
An impossible question to answer for me.
It's like asking "What's you favorite song?"
Gah....
That being said, the answer would have to be qualified as "Who do you think is the cutest [i.e. kawaii] anime girl you have seen or viewed
lately?" ... I think I might be able to answer that.
Should know that I make a difference between kawaii and moe ... kawaii implies adorable and endearing in general without obvious sexual vibes, while moe can have those qualities but includes an element of sexual attraction. To use extreme examples for me, Yune from Ikoku Meiro no Croisee, Flower from Kowarareke no Orgel and Yayoi from The iDOLM@STER are kawaii; Erio, Ryuko and Meme from Denpa Onna to Seishun Otoko are moe.
Of course there is cross-over and such, and I know this is purely personal taste.
That being said to answer the OP with the qualifications above the most recent character that I saw and thought they were almost inhumanly adorable almost to the point of getting hives has got to be Takatsuki Yayoi from iM@S.
But overall? Way too hard a question for me to answer; maybe Shiori from the TWGOK manga/anime series would be a contender? Dunno....