Try opening the map and see if you are indeed at the correct checkpoint. It is quite easy to wander off track (and more fun to do so after all), so it is possible that you are skipping the proper checkpoint and pass through another one.
As for the "Wrong Checkpoint", I do tend to hear it more than the "Checkpoint!" voice, since when you are chasing someone, you don't really care where you both are ;)

Map should be either TAB or M, not sure which one, but the manual should mention the correct key. And the above apply to both games.

Whenever I miss a checkpoint I just keep racing through the track as normal. Eventually you will come upon the one you missed and on the way there you can wreck a few opponents and jump up the score. Most of the time I'm trying to wreck all opponents anyways, but about half the time I end up finishing the race by going through the checkpoints.

When I was much younger I used to go for the "kill all pedestrians" objective to finish the race but I don't have the patience for it any longer.

I find that in the first game, because of the track designs, it is very easy to miss a checkpoint every now and then unless you are really focused on just racing and navigating the tracks.

In some cases at least I'm pretty sure I did go through the right checkpoint, because after going through the 'wrong' one, I went back the same way I came, through the same previous checkpoint again and continued further and the next checkpoint was valid this time.

So... I was thinking if there may be some technical reason why the game wouldn't recognize passing through a checkpoint or something. One thing I noticed once is that when I run over some person just under the checkpoint, I get the bonus notification on screen but not the checkpoint notification. That was the case when I drove back.

Never seen this behaviour on any of the times I've played Carmageddon 1 or 2, but as has already been said, it is very easy to miss checkpoints. The map also shows the next checkpoint as flashing, so you can check that you are going for the right one.

In the Carmageddon games finishing a race is just and option and the checkpoints are mere suggestions :)

The checkpoints do give you a time bonus though, which is handy if the clock is running out ;-)

They don't, they only give money bonus!

Right?

That's true, in classic games (1 and 2) checkpoints gives you only money bonus, no time.

Only in TDR2K checkpoints give you bonus time.

I admit I haven't played it recently, I'll have to go back and check that...

Going after checkpoints....XD Man you guys never cease to crack me up!

Wrong checkpoint means you're playing the game right. ;-)