Update: 2017-02-25 As Dave explained in the comments, the width of airways is defined in Order 8260.3C. You can read the order or my snippet of it.
As near as I can tell, the FARs no longer specify the width of Federal Airways. But that was not always the case. A Google search finds this pdf, which says,
14 CFR Ch. I (1–1–03 Edition)
§ 71.75 Extent of Federal airways.
(1) Each Federal airway includes the airspace within parallel boundary lines 4 miles each side of the center line. Where an airway changes direction, it includes that airspace enclosed by ex- tending the boundary lines of the air- way segments until they meet
And the text of another search is:
The width of a Federal Airway from either side of the centerline is 4 NM.  Gleim #: 4.6.77 Source: FAR 71.75: Unless otherwise specified, Federal Airways …
If you look at the current FARs, there is no §71.75
My first thought is that it is now located in FAA Order 7400.9V but if it is, I can’t find it.
The FAA knowledge tests have variants of this question, and the answer is definitely b.
3. Airway courses are magnetic and distance depicted on charts is in nautical miles (NM). Generally, how wide is a federal airway (within 51 NM of the navaid)?
a. 2 NM each side of centerline
b. 4 NM each side of centerline
c. 6 NM each side of centerline
d. 8 NM each side of centerline
I know that’s the answer because I got it right several times. And the FAA-H-8083-15 Instrument Flying Handbook says:
“Each Federal airway is based on a centerline that extends from one NAVAID or intersection to another NAVAID specified for that airway. A Federal airway includes the airspace within parallel boundary lines 4 NM to each side of the centerline. As in all instrument flight, courses are magnetic, and distances are in NM.”
Another hint is that according to FAR 91.303 “No person may operate an aircraft in aerobatic flight— Within 4 nautical miles of the center line of any Federal airway”.
The AIM refers to the 4 NM width when discussing other topics but never explicitly defines a Federal Airway width.
5-3-5 c. …a course change of more than 40 degrees would exceed the width of the airway or route; i.e., 4 nautical miles each side of centerline.
3-3-3 a. 14 CFR Section 91.177 includes a requirement to remain at least 1,000 feet (2,000 feet in designated mountainous terrain) above the highest obstacle within a horizontal distance of 4 nautical miles from the course to be flown.
So if you are taking a test or get asked by an examiner, the answer is 4 NM, but it would be nice to find the regulation that states this.
Update: The Instrument Flying Handbook has this to day about airways.
The primary means for routing aircraft operating under
IFR is the Federal Airways System. Each Federal airway is
based on a centerline that extends from one navigational aid
(NAVAID)/waypoint/fix/intersection to another NAVAID/
waypoint/fix/intersection specified for that airway. A Federal
airway includes the airspace within parallel boundary lines
4 NM to each side of the centerline. As in all instrument
flight, courses are magnetic, and distances are in NM. The
airspace of a Federal airway has a floor of 1,200 feet AGL,
unless otherwise specified. A Federal airway does not include
the airspace of a prohibited area.