"Mauricio Gugelmin [...]
Pole performance at California, at an average speed of 240.942 mph [387.7586 km/h], was the fastest official lap in auto racing history ... Also had a practice lap of 242.333 mph [389.9972 km/h] prior to qualifying, the fastest unofficial lap in auto racing history ...
[...] Recorded the fastest race lap in the U.S. 500 at Michigan Speedway ..."

Now this was average. The top (trap) speed was (from a post by Barry Posner):

: According to the Omega Timing site (omegatiming.com), the fastest
: trap speed during the Fontana race was 245.528 mph (395.14 km/h)
: by Jimmy Vasser.

: Last year at Michigan, Paul Tracy recorded a trap speed of 
: 256.948 mph (413.52 km/h). The same site gives Adrian
: Fernandez a trap speed of 333 mph, but that *has* to be an error.

: The top trap speed at this year's Michigam 500 was 249.018 mph
: (400.76 km/h) recorded by Richie Hearn. With a Ford motor ;)

The previous (1998) record for F1 was 356.5 km/h (221.5 mph), done by David Coulthard at Hockenheim during the Friday free practices.
http://www.pitlane.com/F1/Races/1998/11GER1998/1998GERt1.html
A Finnish newspaper gave a slightly different speed: 358 km/h (222.45 mph) The second value is probably closer to the truth, since:
"At Hockenheim Norbert Haug said in a interview that they accelerated for 80 meters more (after the TV speed trap) and got close to 360km/h."

Usually the speeds at Monza (just before the first chicane) are a bit higher than at Hockenheim, but not in 1998 (probably due to the rain). I thought that on Friday morning the track was dry enough that top speed could have been uneffected, but the speeds were "low" (331.8 km/h, which is slower than last year).

In fact the highest speed was 340.4 km/h (211.514 mph) by Rubens Barrichello in a Stewart-Ford SF-2 (!) done on Sunday: http://www.pitlane.com/F1/Races/1998/14ITA1998/1998ITAt3.html

BTW, the modern F1 cars are faster than the +1300HP turbo cars of the 1986 qualifying sessions, which reached about 343 km/h at Monza.

The highest speed recorded in an European race was at Le Mans:

The record for top speed in a closed circuit used to be hold by a WM at Le Mans (when Les Hunaudieres was still a 5 km long straight). at about 405-407 Km/h (sources differ on the exact speed).
We had a thread in rec.autos.sport.f1 about that subject around May, 22, 1997.

In that thread John Napper wrote:

: I have checked out the WM story in the contemporary Autosport reports
: and in the 1988 Le Mans yearbook.

: As a small team with a tiny budget they knew they had no chance of
: winning but they had a history of building very low-drag cars which
: were often the quickest on the Mulsanne straight so they decided to
: go for the publicity of being the first car to do 400kph in the race.
: Thus was born 'Project 400'. In 1987 they managed it in pre-race
: testing on an airfield runway but fell some way short at the track.

: They built a new car for 1988 with even lower drag and went for it
: about 3 hours into the race with cooling intakes taped over for
: further drag reduction and Roger Dorchy achieved a speed of 
: 407kph (251mph). The engine was then finished and the car wheeled 
: away at the end of the lap by a happy team. Incidentaly, Michelin
: supplied WM with special narrow tyres to aid the drag reduction
: quest.

240 mph McLaren F1 Road Car Shatters Top Speed Record.

The McLaren F1 has obliterated the production road car record achieving a new official top speed of 240mph/387km'h at the VW Ehra-Lessien proving ground in Germany.

A team of four McLaren F1 road car engineers together with the Technical Director Gordon Murray ran XP5, a standard F1 road car built in 1993, for the top speed record runs. Driven by racing driver Andy Wallace the F1 took just one attempt to break McLaren's previously unofficial top speed of 231mph set at Nardo in 1993. On the third run the car reached a phenomenal 240.1mph/386.7km'h smashing the previously held record of 212mph set by a Jaguar XJ220. The record breaking speed was independently verified by a team of VW technicians.

With a 21km track consisting of two 9km straight sections and banking at either end the facility at Ehra is one of only two in the world where it is possible to attempt top speed records. Whilst the straights stretch out into the distance the circuit is the width of a three-lane motorway leaving little room for error. Driver Andy Wallace described the behaviour of the F1 during the runs - "I'm amazed at how stable it was at 240mph. The forces acting on it when you are going that quickly are not double what they are at 100mph - it's the square speed".

See also: Sydney Morning Herald report of this test.