In the past, constraining the surface composition of near-Earth asteroids (NEAs) has been difficult due to the lack of high quality near-IR spectral data (0.7-2.5 microns) that contain mineralogically diagnostic absorption bands. Here we present visible (0.43-0.95 microns) and near-infrared (0.7-2.5 microns) spectra of nine NEAs and five Mars-crossing asteroids (MCs). The studied NEAs are: 4055 Magellan, 19764 (2000 NF5), 89830 (2002 CE), 138404 (2000 HA24), 143381 (2003 BC21), 159609 (2002 AQ3), 164121 (2003 YT1), 241662 (2000 KO44) and 2007 ML13. The studied MCs are: 1656 Suomi, 2577 Litva, 5407 (1992 AX), 22449 Ottijeff and 47035 (1998 WS). The observations were conducted with the NTT at La Silla, Chile, the 2.2 m telescope at Calar Alto, Spain, and the IRTF on Mauna Kea, Hawaii. The taxonomic classification (Bus system) of asteroids showed that all observed MC asteroids belong to the S-complex, including the S, Sr and Sl classes. Seven of the NEAs belong to the S-complex, including the S, Sa, Sk and Sl classes, and two NEAs were classified as V-types. The classification of the NEA 164121 (2003 YT1) as a V-type was made on the basis of its near-infrared spectrum since no visible spectrum is available for this asteroid. A mineralogical analysis was performed on six of the asteroids (those for which near-IR spectra were obtained or previously available). We found that three asteroids (241662 (2000 KO44), 19764 (2000 NF5), 138404 (2000 HA24)) have mafic silicate compositions consistent with ordinary chondrites, while three others (4055 Magellan, 164121 (2003 YT1), 5407 (1992 AX)) are pyroxene-dominated basaltic achondrite assemblages. In the case of 5407 (1992 AX) we found that its basaltic surface composition contrasts its taxonomic classification as a S-type.