There are plenty of 16-bit era games that i've played but my most favorite is Crazy Cars III (1992).
While a though game to beat, there's plenty of features that make the gaming enjoyable and at times, frustrating too.
Few of the features include: non-visual damage to your car (except smoking when damage gets high), car upgrades (top speed, handling, boost etc), police pursuits, betting system (to increase payout if you win), different scenery for each race, traffic cars on the road, plenty of opponents (19 in every race), good sounds (for that era) etc.
Here's also a gameplay video with good explanations on how the game works. The video covers the 4th division while there's also 3rd, 2nd and 1st division to play through.