Your tires are the most important part of your bike - on road or track. They're what keep you connected to the road, they deal with the huge braking forces to stop you, they hold you to every corner and they cling on for grim life when you open the throttle to accelerate. They also have a massive effect on how your bike performs, affecting handling, geometry and how the bike steers.
Just as your tires can make your bike feel fantastic, if your tires are shit you're not getting the most from your bike, it's as simple as that. And, of course, 'bad' tires can be downright dangerous. Therefore we have a few things to you want to consider when you roll your road bike out of the garage...
Under-inflated tires, this is the common one. What are the chances your tires are incorrectly inflated right now? The loss of pressure can be subtle and over a long period it can be hard to notice and change.
Go out, check the pressure, correct it and see if you don't notice an improvement in the front end of your bike. Basically, not enough air in the front means it'll turn more slowly because the sidewall and carcass are deforming more than it should, which is why it feels 'mushy'.
Over-inflated tires. Baring in mind that we are talking about road bike tires in road conditions here, an over-inflated tire will do the opposite of a under-inflated tire. The carcass and sidewall won't deform enough as you hit bumps, corner and brake, reducing the size of the contact patch and, ultimately, grip. Do you want less grip on the road - ever? No.
The 'wrong' tire. Semi-fast road rider are you? Bit of a Sunday blaster? Think you need track tires for your road riding? Bollocks. The more aggressive 'pointy' profile of a track-bias tire means it'll be less stable on bumpier roads and under braking. A big fan of instability and head shakes are you? Don't be so self-important and think you 'need' the stickiest tires available. Manufacturers spend millions developing sporty road tires that work in the real world you know.