Are there any C++ (or C) libs that have NumPy-like arrays with support for slicing, vectorized operations, adding and subtracting contents element-by-element, etc.?
Here is several free softwares that would suits your needs.
The GNU Scientific Library is a GPL software written in C. It thus have a C-like allocation and way of programming (pointers, etc.). With the GSLwrap, you can have a C++ way of programming, while still using the GSL. GSL has a BLAS implementation, but you can use ATLAS instead of the default CBLAS, if you want even more performances.
The boost/uBLAS library is a BSL library, written in C++ and distributed as a boost package. It is a C++-way of implementing the BLAS standard. uBLAS comes with a few linear algebra functions, and there is an experimental binding to ATLAS.
eigen is a linear-algebra library, written in C++, distributed under the LGPL3 (or GPL2). It's a C++ way of programming, but more integrated than the two others (more algorithms and data structures are available). Eigen claim to be faster than the BLAS implementations above, while not following the de-facto standard BLAS API. Eigen does not seems to put a lot of effort on parallel implementation.
Armadillo is LGPL3 library, in C++. It has binding for LAPACK (the library used by numpy). It uses recursive templates and template meta-programming, which is a good point (I don't know if other libraries are doing it also?).
These alternatives are really good if you just want to get data structures and basic linear algebra. Depending on your taste about style, license or sysadmin challenges (installing big libraries like LAPACK may be difficult), you may choose the one that best suits your needs.