The online racing simulator
I have not "raced" IRL, but I do a lot of track days and have helped out a lot of actual racers. I use my speedo to check corner exit speeds all the time. Sometimes the tach is more useful, sometimes not. And I've rarely seen a race car without a functioning speedo for long. In fact, if they're allowed, even club racers have usually switched over to a Stack dash or similar for data logging and better info, and you can bet that has a big 'ol digital speedo on it too.

Most professional race cars have a digital speedo, at least all the stuff I've seen in the US. Once you've figured out a track 100% or are in a racing environment, then, sure it might not be much good. But while testing and learning tracks, it's just another tool to help you improve.
When I raced karts I would look at my mycron (http://www.dataspares.com/products/AIM/mycron3.jpg)

multiple times every lap any time I wasn't racing nose to tail with someone. I'd look down for the RPM at the end of the long straights to see if the gearing needed to be changed (expensive little shits to fix when you explode a piston). I'd constantly be looking at the temps driving out of the slowest corners, slow = hot, and of course there were the split times and finish line

I'd always be looking at the split times, even during a race.

I was going like 75 mph into turn 1, so looking down at the tach wasn't really that much different than it would be to do it in a car, and I whole heartedly believe you could kill yourself easier in a kart than a car.

Never had a speedo on the karts though, even though you could purchase one. No reason to have one...if you had a tach, you could easily tell if you were going faster or not...but you could usually tell that from the seat of your pants anyways :P
Quote from Victor :And yes, very good chance i'll be going again next year. And not just to Zandvoort i hope.

Cool! I'll be on the lookout for that 350Z then!
#54 - _ak
For bikes many tracks have no speedo rule. So riders just tape it out on stock (or little modified) bikes.
Usually no.

The only time is to check my exit speed in some important corners. Other than that, a speedo is pretty useless.

Furthermore, karts don't - generally - have a speedo.

FGED GREDG RDFGDR GSFDG