The current UA fleet has an average of 13.7 years; will likely drop fairly significantly with the announced and all-but-certain retirements (757, 747, oldest of the 73X and A32X).

1 Allegiant Air 23.0
2 Delta Air Lines 15.8
3 Aeromexico 15.2
4 Southwest Airlines 14.7 (Edit - roughly tied with American Airlines)
5 US Airways 14.6
6 United Airlines 13.7
7 Cathay Pacific 13.0
8 Asiana Airlines 12.6
9 Lufthansa 12.4
10 Norwegian Air Shuttle 12.3
11 Thai Airways International 12.2
12 Air France 11.5
13 EVA Air 11.3
13 Garuda Indonesia 11.3
15 Air New Zealand 11.2
15 Japan Airlines 11.2
15 Philippine Airlines 11.2
18 China Airlines 11.0
19 Alaska Airlines 10.6
20 Hainan Airlines 10.1
21 Korean Air 9.9
22 ANA - All Nippon Airways 9.8
23 Gol 9.5
24 KLM Royal Dutch Airlines 9.4
25 WestJet 9.3
26 Aeroflot Russian Airlines 8.9
27 Air China 8.7
28 Turkish Airlines 8.4
29 Avianca 8.0
30 China Eastern Airlines 7.5
30 China Southern Airlines 7.5
30 Singapore Airlines 7.5
33 Virgin Australia 7.1
34 Qatar Airways 7.0
35 Copa Airlines 6.5
36 LAN Airlines 6.1
37 TACA International Airlines 6.0
38 Spirit Airlines 5.7
39 Ryanair 5.0
40 JetBlue Airways 4.7
41 EasyJet 4.0
42 Air Arabia 3.0
42 AirAsia 3.0

Source: Bloomberg; Planespotters.net for AA data