Some dances that full under the banner of ballroom dancing:
the Waltz
the Tango
Salsa
Paso Dolbe
Boxstep
Jive
Foxtrot
Cha-Cha/Cha-Cha-Cha
Rhumba/Rumba
...and many variations thereof.
Ballroom dancing traditionally has the male leading, and involves two people. Both partners are usually in constant physical contact.