Consumer Reports obtained the numbers from the FCC, and leading for most
consumer complaints was AT&T Wireless.

http://biz.yahoo.com/rc/040511/telecoms_wireless_complaints_1.html

The order was:

AT&T Wireless

Sprint PCS

T-Mobile

Cingular

Nextel

Verizon

" After billing problems consumers complained most about number
transfers to other carriers, service quality, contracts and how wireless
companies marketed and advertised their services, the Consumers union
said. "

===============================

As AT&TWS has more customers than SprintPCS, it might be expected to
generate more complaints, so any raw numbers would have to be normalized
taking number of customers into account.

It's like the meaningless statistic that Toyota Camry is the most stolen
car in the United States. The Toyota Camry sells more cars than any
other nameplate, so it might be expected to be at the top of the list.

So how many cars are stolen per 1000 sold?

How many Consumer Complaints are there to the FCC per million cellular
customers is the question to ask.

One obvious conclusion without raw numbers. Verizon has the MOST
customers, and it had the fewest total complaints. It has to come best.

====
The FCC has not separately released (that I can find) this information.
It did release data about complaints about porting:

There it reported:

  The carriers most often mentioned in the complaints as either the
carrier ported from or the carrier ported to are:  AT&T Wireless (3104);
Sprint PCS (1712); Verizon Wireless  (1059);  T-Mobile (991);  Cingular
Wireless (991); and Nextel (501).   Many of the complaints concern more
than one carrier so the total number of complaints received is smaller
than the number of times a carrier is mentioned in a complaint.

http://hraunfoss.fcc.gov/edocs_public/attachmatch/DOC-246604A1.doc