Some of the technological applications of superconductivity include:
The biggest application for superconductivity is in producing the large-volume, stable, and high-intensity magnetic fields required for MRI and NMR. This represents a multi-billion-US$ market for companies such as Oxford Instruments and Siemens. The magnets typically use low-temperature superconductors (LTS) because high-temperature superconductors are not yet cheap enough to cost-effectively deliver the high, stable, and large-volume fields required, notwithstanding the need to cool LTS instruments to liquid helium temperatures. Superconductors are also used in high field scientific magnets.
Particle accelerators such as the Large Hadron Collider can include many high field electromagnets requiring large quantities of LTS. To construct the LHC magnets required more than 28 percent of the world's niobium-titanium wire production for five years, with large quantities of NbTi also used in the magnets for the LHC's huge experiment detectors. 
Conventional fusion machines (JET, ST-40, NTSX-U and MAST) use blocks of copper. This limits their fields to 1-3 Tesla. Several superconducting fusion machines are planned for the 2024-2026 timeframe. These include ITER, ARC and the next version of ST-40. The addition of High Temperature Superconductors should yield an order of magnitude improvement in fields (10-13 tesla) for a new generation of Tokamaks. 
The commercial applications so far for high temperature superconductors (HTS) have been limited.
HTS require only liquid nitrogen, not liquid helium, to cool to superconducting temperatures. However, the problem with HTS technology is that the currently known high temperature superconductors are brittle ceramics which are expensive to manufacture and not easily formed into wires or other useful shapes.  Therefore, the applications for HTS have been where it has some other intrinsic advantage, e.g. in
HTS has application in scientific and industrial magnets, including use in NMR and MRI systems. Commercial systems are now available in each category. 
Also one intrinsic attribute of HTS is that it can withstand much higher magnetic fields than LTS, so HTS at liquid helium temperatures are being explored for very high-field inserts inside LTS magnets.
Promising future industrial and commercial HTS applications include Induction heaters, transformers, fault current limiters, power storage, motors and generators, fusion reactors (see ITER) and magnetic levitation devices.
Early applications will be where the benefit of smaller size, lower weight or the ability to rapidly switch current (fault current limiters) outweighs the added cost. Longer-term as conductor price falls HTS systems should be competitive in a much wider range of applications on energy efficiency grounds alone. (For a relatively technical and US-centric view of state of play of HTS technology in power systems and the development status of Generation 2 conductor see Superconductivity for Electric Systems 2008 US DOE Annual Peer Review.)
The Holbrook Superconductor Project, also known as the LIPA project, is a project to design and build the world's first production superconducting transmission power cable. The cable was commissioned in late June 2008 by the Long Island Power Authority (LIPA). The suburban Long Island electrical substation is fed by about 600-meter-long underground cable system consists of about 99 miles (159 km) of high-temperature superconductor wire manufactured by American Superconductor, installed underground and chilled with liquid nitrogen greatly reducing the costly right-of-way required to deliver additional power.  In addition, the installation of the cable eluded strict permission complications for overhead power lines, and offered a solution for the public's concerns for overhead power lines.  
American Superconductor was chosen for the Tres Amigas Project, the United States’ first renewable energy market hub.  The Tres Amigas renewable energy market hub will be a multi-mile, triangular electricity pathway of superconductor electricity pipelines capable of transferring and balancing many gigawatts of power between three U.S. power grids (the Eastern Interconnection, the Western Interconnection and the Texas Interconnection). Unlike traditional powerlines, it will transfer power as DC instead of AC current. It will be located in Clovis, New Mexico.
Essen, Germany has the world's longest superconducting power cable in production at 1 kilometer. It is a 10 kV liquid nitrogen cooled cable. The cable is smaller than an equivalent 110 kV regular cable and the lower voltage has the additional benefit of smaller transformers.  
An aluminium plant in Voerde, Germany plans to use superconductors for cables carrying 200 kA, citing lower volume and material demand as advantages.  
Magnesium diboride is a much cheaper superconductor than either BSCCO or YBCO in terms of cost per current-carrying capacity per length (cost/(kA*m)), in the same ballpark as LTS, and on this basis many manufactured wires are already cheaper than copper. Furthermore, MgB2 superconducts at temperatures higher than LTS (its critical temperature is 39 K, compared with less than 10 K for NbTi and 18.3 K for Nb3Sn), introducing the possibility of using it at 10-20 K in cryogen-free magnets or perhaps eventually in liquid hydrogen.[ citation needed] However MgB2 is limited in the magnetic field it can tolerate at these higher temperatures, so further research is required to demonstrate its competitiveness in higher field applications.
Exposing superconducting materials to a brief magnetic field can trap the field for use in machines such as generators. In some applications they could replace traditional permanent magnets.