Quantum field theories with asymptotic freedom QCD is the best-known example of theories with negtive beta function, i.e., coupling constant decreases when increasing energy scale. I have two questions about it:
(1) Are there other theories with this property? (non-Abelian gauge theory, principal chiral field, non-linear sigma model, Kondo effect, and ???)
(2) Are there any simple (maybe deep) reason why these theories are different from others? It seems that the non-linear constraint of the non-linear sigma model (and principal chiral model) is important, but I have no idea how to generalize this argument to other theories.
 A: As gih correctly pointed out, there are a lot of QFTs in low dimensions which are asymptotically free.  
In 3d, for example:


*

*Scalar $\phi^4$ field theory in 3d is asymptotically free.  Renormalization flow increases the quartic coupling, taking you away from the free theory.  

*Likewise, the 3d Gross-Neveu model (Dirac fermions with a 4-fermion interaction) is also asymptotically free.  The 4-fermion interaction is relevant in 3d (rather than non-renormalizable, as it is in 4d).

*Plain old 3d Yang-Mills gauge theory in 3d is asymptotically free.  (Even better, you can set things up so that the YM kinetic term itself is irrelevant, giving you a topological theory at low energies.)


It's not hard to combine these basic models to get more complicated but still asymptotically free models.
To address the 2nd part of your question:  There's probably not anything model-specific going on here.  It's just that the basic ingredients in these lower dimensional theories are better behaved.
A: One example would be $\varphi^3$ theory, which is treated extensively in Srednicki.
