blockcipher-based MACs with variable length that are UF-CMA secure? There are may papers and notes explain why CBC-MAC is only UF-CMA secure for fix length messages. Are there any other blockcipher-based (blockcipher and hash combined included) MACs that is UF-CMA secure with variable length messages?
Are there any other blockcipher-based (blockcipher and hash combined included) MACs that is UF-CMA secure with variable length messages?

Sure.
The most famous one is probably CMAC (a.k.a. OMAC1) which is essentially CBC-MAC but with a key-dependent secret random value XOR'ed with the last message block1.
Alternatively there is a general theorem that $F_k(H_\kappa(m))$ is a PRF (and thus a secure MAC) as long as $F$ is a secure fixed-length PRF and $H$ is a collision-resistant (potentially-keyed) hash function. You can find a proof of this e.g. in the Boneh-Shoup book (section 7). This e.g. brings the (parts of) the security proofs for HMAC and PMAC. Additionally you can somewhat easily define MACs based on this, e.g. $\operatorname{AES}_{k_1}(\operatorname{GHASH}_{k_2}(m\|\operatorname{len}(m)))$.

1: This is an accurate enough simplification of CMAC. It actually uses more than one such random value for messages that are not a multiple of the block length