It is possible for any thunderstorm to produce a tornado if conditions in the troposphere are right. However, tornadoes that do not develop within a supercell thunderstorm tend to be weaker and more short-lived than those that do.
Two types of non-supercell tornadoes that can form are landspouts and gustnadoes.
Landspouts are similar to waterspouts. They form when winds at lower levels in the troposphere converge at the same time as a strong updraft occurs, creating a generally weak rotating funnel.
A gustnado forms on the leading edge of rapidly moving cool air caused by thunderstorm downdrafts known as gust fronts. Sometimes conditions are favorable for winds to briefly spin up, create a gustnado, then quickly dissipate.