One must wash before each tefilah (S"A 92:4, 233:2). Do you need to wash 3 times before davening, or is 1 time sufficient?
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The washing for tefillah is because of cleanliness, not purity (Magen Avraham 93:3, Machtzis Hashekel there). Washing for cleanliness does not require three pourings, as that is for Tahara purposes. This is why בדיעבד even any non-liquid cleaning substance such as a rock can be used (S.A. ibid).
Although the common practice does seem (to me, after seeing many people washing before mincha) to be to wash three times, but common practice seems to be to do so at many times when it is not required.
Edit: The above answer was assuming that you are washing exclusively because of Tefillah even though you know your hands are clean. If you are washing for Tefillah because you may have touched a sweaty part of your body, there are opinions (Levush 4:18, Shulchan Aruch HaRav 128:27, others) that hold this creates a Ru'ach Ra'ah (evil spirit) and you would have to wash according to the level required for such, which is 3 times on each hand, switching off hands.
Regarding the cup discussion (in the comments), the Piskei Teshuva in Siman Daled cites the Shulchan Aruch as saying you should use a cup for washing for all Tefillos, but his citation is to 4:7, which is about washing in the morning, not washing for Tefillah.