SIMD (Single Instruction Multiple Data) instructions and their compiler intrinsics are widely supported by modern processors to accelerate performance-critical tasks. SIMD intrinsic programming, a trade-off between coding productivity and high performance, is widely used in the development of mainstream performance-critical libraries and daily computing tasks. Large Language Models (LLMs), which have demonstrated strong and comprehensive capabilities in code generation, show promise in assisting programmers with the challenges of SIMD intrinsic programming. However, existing code-generation benchmarks focus on only scalar code, and it is unclear how LLMs perform in generating vectorized code using SIMD intrinsics. To fill this gap, we propose SimdBench, the first code benchmark specifically designed for SIMD-intrinsic code generation, comprising 136 carefully crafted tasks and targeting five representative SIMD intrinsics: SSE (x86 Streaming SIMD Extension), AVX (x86 Advanced Vector Extension), Neon (ARM Advanced SIMD Extension), SVE (ARM Scalable Vector Extension), and RVV (RISC-V Vector Extension). We conduct a systematic evaluation (measuring both correctness and performance) of 18 representative LLMs on SimdBench, resulting in a series of novel and insightful findings. Our evaluation results demonstrate that LLMs exhibit a universal decrease in pass@k during SIMD-intrinsic code generation compared to scalar-code generation. Our in-depth analysis highlights promising directions for the further advancement of LLMs in the challenging domain of SIMD-intrinsic code generation. SimdBench is fully open source at https://anonymous.4open.science/r/SimdBench-1B3F/ to benefit the broader research community.