This paper proposes two types of sparse arrays (SAs) for enabling near-field communications (NFC) with reduced hardware and energy costs. The first SA is the linear sparse array (LSA), which has a larger inter-antenna spacing than a uniform linear array (ULA). The second SA is the extended coprime array (ECA), which consists of two LSA subarrays with different inter-antenna spacings. The paper characterizes the near-field beam patterns of both SAs and proposes hybrid beamforming designs to mitigate inter-user interference (IUI). For the LSA, the beam pattern has a main-lobe with a narrower beam-width and smaller beam-depth compared to the ULA. However, the LSA generates multiple grating-lobes with high beam power, which can cause significant IUI. To address this, an efficient hybrid beamforming design is proposed to minimize the difference between the designed hybrid beamforming and the optimal digital beamforming. For the ECA, the beam pattern has a main-lobe with a similar beam-width and beam-depth to the LSA. However, the ECA has more grating-lobes due to the larger inter-antenna spacing of the two subarrays. The beam-heights of the ECA grating-lobes are much smaller than those of the LSA, due to the offset effect of the two subarrays. This results in better worst-case user rate performance for the ECA compared to the LSA. A customized two-phase hybrid beamforming design is proposed for the ECA, which first uses the maximum ratio transmission (MRT) beamformer to maximize the received power at each user and then designs the digital beamforming to cancel the residual IUI. Numerical results show that both the LSA and ECA achieve significant rate performance gains over the ULA when users are located at the same or similar angles. The ECA achieves even higher sum-rate when users are located at grating-lobes due to its lower grating-lobe beam-heights. The proposed SAs and hybrid beamforming designs are shown to be effective in reducing IUI and improving the performance of NFC systems.This paper proposes two types of sparse arrays (SAs) for enabling near-field communications (NFC) with reduced hardware and energy costs. The first SA is the linear sparse array (LSA), which has a larger inter-antenna spacing than a uniform linear array (ULA). The second SA is the extended coprime array (ECA), which consists of two LSA subarrays with different inter-antenna spacings. The paper characterizes the near-field beam patterns of both SAs and proposes hybrid beamforming designs to mitigate inter-user interference (IUI). For the LSA, the beam pattern has a main-lobe with a narrower beam-width and smaller beam-depth compared to the ULA. However, the LSA generates multiple grating-lobes with high beam power, which can cause significant IUI. To address this, an efficient hybrid beamforming design is proposed to minimize the difference between the designed hybrid beamforming and the optimal digital beamforming. For the ECA, the beam pattern has a main-lobe with a similar beam-width and beam-depth to the LSA. However, the ECA has more grating-lobes due to the larger inter-antenna spacing of the two subarrays. The beam-heights of the ECA grating-lobes are much smaller than those of the LSA, due to the offset effect of the two subarrays. This results in better worst-case user rate performance for the ECA compared to the LSA. A customized two-phase hybrid beamforming design is proposed for the ECA, which first uses the maximum ratio transmission (MRT) beamformer to maximize the received power at each user and then designs the digital beamforming to cancel the residual IUI. Numerical results show that both the LSA and ECA achieve significant rate performance gains over the ULA when users are located at the same or similar angles. The ECA achieves even higher sum-rate when users are located at grating-lobes due to its lower grating-lobe beam-heights. The proposed SAs and hybrid beamforming designs are shown to be effective in reducing IUI and improving the performance of NFC systems.