Concrete and concrete blocks are not designed to bond with tape. Some construction adhesives and epoxies will work with concrete, but because of the porous materials from which concrete is made, tape rarely works well to adhere objects. However, if you need to use tape on your concrete blocks, choose a tape that is designed for concrete and will not interfere with other plans for your concrete blocks.
Masking tape is one of the best tapes to use on concrete blocks. Normal masking tape will have minimal effectiveness, but there are many variations to masking tape, and some of them are designed specifically to work on surfaces like concrete block. Look for highly adhesive masking tape that specifies potential use on concrete blocks and wood siding.
Seam tape is used to put up vapor barriers on concrete walls. It is a tough tape designed for long-term adherence. Even if you are not using vapor barriers and are trying to attach objects to individual blocks instead of an entire wall, seam tape is still a good bet for strong adherence.
Carpet tape is designed to hold objects to smooth floor surfaces, including rugs and mats. There are several types of carpet tape, but some versions are designed especially for concrete. This is another type of versatile tape that can work even if you want to attach something besides a rug.
Be very careful when taping anything to decorated concrete, or concrete you are planning to decorate in the future. Concrete with acid stain or sealant should never be taped. The tape will rip off the sealant and create a place for moisture to gather under the concrete surface, ruining the design. If you plan on decorating concrete block or tile, you should not attach anything to the surface.