Yes, this is called superelevation.
The roads at the bends are built in such a way that the outside of the bend is higher than the inside. Gravity forces (μmgsinθ) will push against the centripetal acceleration and in the best of all cases, they balance out.
The centripetal acceleration is always present, but it is just balanced to avoid skidding outwards, especially in icy weather.
Read more about it here:
http://techalive.mtu.edu/modules/module0003/Superelevation.htm
Is it possible for a car to move in a circular path in such a way that it has a tangential acceleration but no centripetal acceleration?
2 answers
No. hhhhmmmmm.
Yes, in the special case when tangential velocity is zero for an instant.
Yes, in the special case when tangential velocity is zero for an instant.