Citylink provide express services between Galway and:

Dublin and Dublin Airport
Limerick, Cork and Cork Airport
Shannon Airport
Clifden, Connemara

http://www.citylink.ie
1890 28 08 08
+353 (0)91 564163 (outside Ireland)

Bus Eireann operate express services between Galway and:

Dublin
Cork
Belfast
Dundalk, Louth
Derry
Rosslare, Wexford
Ballina, Mayo
Lahinch, Clare
Limerick
Sligo
Kerry

http://www.buseireann.ie

(West of Ireland) +353 (0)91 563555