Accelerating program performance via SIMD vector units is very common in modern processors, as evidenced by the use of SSE, MMX, VSE, and VSX SIMD instructions in multimedia, scientific, and embedded applications. To take full advantage of the vector capabilities, a compiler needs to generate efficient vector code automatically. However, most commercial and open-source compilers fall short of using the full potential of vector units, and only generate vector code for simple innermost loops. In this paper, we present the design and implementation of an auto-vectorization framework in the backend of a dynamic compiler that not only generates optimized vector code but is also well integrated with the instruction scheduler and register allocator. The framework includes a novel compile-time efficient dynamic programming-based vector instruction selection algorithm for straight-line code that expands opportunities for vectorization in the following ways: (1) scalar packing explores opportunities of packing multiple scalar variables into short vectors; (2) judicious use of shuffle and horizontal vector operations, when possible; and (3) algebraic reassociation expands opportunities for vectorization by algebraic simplification. We report performance results on the impact of auto-vectorization on a set of standard numerical benchmarks using the Jikes RVM dynamic compilation environment. Our results show performance improvement of up to 57.71% on an Intel Xeon processor, compared to non-vectorized execution, with a modest increase in compile time in the range from 0.87% to 9.992%. An investigation of the SIMD parallelization performed by v11.1 of the Intel Fortran Compiler (IFC) on three benchmarks shows that our system achieves speedup with vectorization in all three cases and IFC does not. Finally, a comparison of our approach with an implementation of the Superword Level Parallelization (SLP) algorithm from [21], shows that our approach yields a performance improvement of up to 13.78% relative to SLP.