List of rivers of Jordan
This is a list of rivers in Jordan. This list is arranged by drainage basin, with respective tributaries indented under each larger stream's name.  Many of these rivers are seasonal.

Dead Sea
Rivers and streams flowing into the Dead Sea:

Jordan River with affluents
The Jordan River is the major river flowing into the Dead Sea from the north. It also is the northern part of the western border of Jordan. Its affluents are listed from north to south.
Jordan River
Yarmouk River - largest tributary of the Jordan and forms part of the northern border of Jordan with Syria and Israel. Flows into the Jordan just south of the Sea of Galilee
Wadi al-'Arab
Wadi Ziqlab
Wadi al-Yabis (biblical Chorath)
Wadi Kafranja or Kufrinjah, passing near Ajloun
Zarqa River (biblical Jabbok) - second largest tributary of the Jordan, flows in about half way between the Sea of Galilee and the Dead Sea
Wadi Zulayl or Dhuleil
Wadi Shu'ayb or Sha'eb
Wadi al Gharabah
Wadi ar-Ramah
Wadi al Kafrayn
Wadi as-Seer ("Valley of the Orchards" near Amman)

Dead Sea direct affluents
Rivers and streams that flow directly into the Dead Sea are:
Wadi Zarqa Ma'in (Wadi Zarqa' Ma'in, Wadi Zarqa-Ma'in)
Wadi Mujib (biblical Arnon)
Wadi al-Haydan
Wadi an-Nukhaylah
Wadi al-Hafirah
Wadi ash-Shuqayq
Wadi al-Karak
Wadi Arabah (Wadi al-Jayb) - the valley to the south of the Dead Sea and also the southern border with Israel
Wadi al-Hasa (biblical Zered)  
Wadi al-Fidan
Wadi al-Buwayridah
Wadi Musa, passing through the same-name town and ancient Petra

Red Sea (Gulf of Aqaba)
Streams flowing into the Red Sea's Gulf of Aqaba:
Wadi Yitm
Wadi Rum

Syrian Desert
Wadis in the Jordanian part of the Syrian Desert:
Wadi Sirhan
Far Wadi al-Abyad
Wadi Fakk Abu Thiran
Wadi al-Fukuk
Wadi al-Hasah
Wadi al-Gharra
Wadi Ba'ir
Wadi al Makhruq
Wadi al Jashshah al Adlah
Wadi Rijlat
Wadi al Ghadaf
Wadi al Janab

Qa al-Jafr
A "qa" is a mudflat.
Wadi Abu Safah
Wadi al-Buraykah
Wadi Abu Tarafah
Wadi Abu 'Amud
Wadi al-Jahdaniyah
Wadi Kabid
Wadi al-'Unab

References

Rand McNally, The New International Atlas, 1993.
 GEOnet Names Server

Jordan
Rivers