Shrek 2 is the best of the Shrek series. While the first Shrek was just okay and Shrek the 3rd was "blah", this film manages to improve on the first Shrek in almost every way. I'd almost go so far as to call Shrek 2 a "good movie".
The highlight of Shrek 2 is the animation. They brought in James Baxter to supervise the animation and also brought in quite a few of their 2D crew in to animate. The results are great. The animation on the Shrek character is VASTLY improved. The background and side human characters, while still not perfect, are not as stiff looking. The animation is improved on all around.
The story of Shrek 2 is kind of a "meet the parents" type story and I think it worked rather well. There manages to be some touching moments and a lot of laughs. That combined the expert animation of James Baxter makes for a whopping good time.
The new characters are pretty good as well. Antonio Banderas (parodying his role in the Zorro films) as Puss in Boots is funny, Julie Andrews and John Cleese as the King and Queen are both excellent, Rupert Everett and Jennifer Saunders and Prince Charming and the Fairy Godmother are good as well.
Now, it's not all good. The storytelling problems I had with the first Shrek are still there albeit not as abundant as the first Shrek.
I still feel it relies too much on big name actors to sell the film, mean-spirited fairytale/Disney parodies, and "adult" (or rather: frat-boy) humor which is tasteless in my opinion.
So, in conclusion, while it's nowhere near the quality of a Pixar film, it's a fun and enjoyable romp.