GUE, GOE, hermitian/symmetric wigner matrices, ... already known with some mild assumptions. but is there any this kind of results without independent entries condition. thanks a lot.

Another example is the adjacency matrix of a random regular graph. Here the entries are $0,1$ but the row sums and column sums must all be equal. For some properties of this matrix, see http://arxiv.org/pdf/1011.6646.pdf 


Of course there is: For example: this paper by Lubinsky describes universality for a special class of tridiginal matrices. For example the condition offdiagonals $\equiv 1$ and entries on the diagonal are in $\ell^1(\mathbb{Z})$ would suffice. So the matrices are $$ H_N = \begin{pmatrix} b_1 & 1 & \\\ 1 & b_2 & 1 & \\\ & 1 & b_3 &1 & \\\ & & \ddots & \ddots & \ddots \\\ & & & 1 & b_N \end{pmatrix} $$ with $\sum_{n=1}^{\infty} b_n < \infty$. This can be further generalized see: AvilaLastSimon. Of course all these results are for special tridiagonal matrices (Jacobi operators). Last, there is also the work by Deift et al. See the book. 


the classic example is Dyson's circular ensemble of random unitary matrices (distributed uniformly with respect to the Haar measure); in the limit of large matrix size the correlation function of the eigenvalues tends to a universal limit. 


There are results on symmetric Gaussian matrices where the entries are dependent but the depedencies become weaker and weaker as the size of the matrix grows. See e.g. http://arxiv.org/pdf/0707.2333.pdf and the references therein. 

