What medications may pilots take while flying?
AOPA has the best database that I know of, but you have to be a member to view it.  They have some free information on their Medications page though. 

There they talk about FAA Policy, and it starts with:


  The Federal Aviation Regulations include no specific references to
  medication usage. FAR 61.53 prohibits acting as pilot-in-command or in
  any other capacity as a required pilot flight crewmember, while that
  person:
  
  
  Knows or has reason to know of any medical condition that would make the person unable to meet the requirement for the medical certificate
  necessary for the pilot operation, or:
  Is taking medication or receiving other treatment for a medical condition that results in the person being unable to meet the
  requirements for the medical certificate necessary for the pilot
  operation. Further, FAR 91.17 prohibits the use of "any drug that
  affects the persons faculties in any way contrary to safety."
  


AMAS (Aviation Medicine Advisory Service) also has a list (which is free) but I don't think that it is organized as well.  They are recommended by ALPA and NBAA though.

The most important thing though, of course, is to self evaluate and make sure that you don't fly if you are having any adverse reactions from the medication, or the underlying condition that you are taking the medicine for.

Any list that you consult has to be used only as a guide though, and not a carte-blanche approval.  Individual people can have reactions even to medications that are considered "safe" and "allowed" by the FAA, and this is why they don't list specific medications that they allow.  The FAA has a brochure called Medications and Flying, and one part of it has a few things to consider before taking any medication:


  First, consider the underlying condition  that you are treating. What
  will be the  consequences if the medication doesn’t work  or if it
  wears off before the ﬂight is over?  A good general rule to follow is
  not to ﬂy  if you must depend on the medication to  keep the ﬂight
  safe. In other words, if the  untreated condition is one that would
  prevent  safe ﬂying, then you shouldn’t ﬂy until the  condition
  improves — whether you take the  medication or not.
  
  Second, you must consider your reaction to  the medication. There
  are two broad categories  of medication reactions. One is a unique
  reaction  based on an individual’s biological make-up.  Most people
  don’t have such reactions but  anyone can, given the right medication.
  Because  of this, you should NEVER ﬂy after taking any  medication
  that you have not taken before. It  is not until after you have taken
  the medication  that you will ﬁnd out whether you have this  uncommon
  and unexpected reaction to the  medication.
  
  Third, consider the potential for adverse  reactions, or side
  effects — unwanted reactions  to medications. This type of reaction is
  quite common, and the manufacturer of the  medication lists these on
  the label. You MUST  carefully read all labeling. If you don’t have 
  access to the label, then don’t ﬂy while using the  medication. 
  
  Look for such key words as lightheadedness,  dizziness, drowsiness, or
  visual disturbance. If  these side effects are listed or if the label
  contains  any warning about operating motor vehicles or  machinery,
  then you should not ﬂy while using  the medication. 
  
  Side effects can occur at any time, so even if  you’ve taken the same
  medication in the past  without experiencing side effects, they could
  still  occur the next time. For this reason, you must  never ﬂy after
  taking a medication with any of  the above-noted side effects.