Phoenix X - From the 737 300 manual 'If winds are greater than expected when actually flying the turn, LNAV can command up to 35 degree of bank.
I presume the NG is the same or similar.
I do find the classic A/P flies the plane badly, especially in climbs and descents, and on single channel approaches. However, it is extremely well designed in terms of the pilot interface. It is very intuitive and you never find it doing something unexpected - 'what's it doing now' is very rarely heard on a 737 flight deck.
The FMS (U7.5 onwards) is superb, and far superior to the Airbus (no fix page etc).