Network Function Virtualization (NFV) and Software-Defined Networking (SDN) have been envisioned an essential milestone in the evolution of communication networks. Their integration provides a more flexible and easier manageable software-based network environment that induces high expectations for reducing capital expenditures (CAPEX) and operational costs (OPEX) of network service providers. They also introduce technical challenges. One such challenge is to manage the placement of VNFs and to steer the data traffic of each NFV-enabled request through its specified network functions. In this paper, we opportunistically adopt the flexibility and cost-efficiency of VNF and SDN for NFV-enabled request admissions in SDNs and formulate profit maximization problems for static and dynamic NFV-enabled request admissions. We first provide an integer linear programming (ILP) solution to the problem in the static version if the problem size is small; otherwise, we devise a fast approximation algorithm with a provable approximation ratio for the static request admissions. We then propose an efficient online algorithm for dynamic request admissions, by leveraging VNF instance migrations and idle VNF releases back to the system. We finally evaluate the performance of the proposed algorithms through experimental simulations. Simulation results demonstrate that the proposed algorithms are very promising.