Heart

ParametricPlot[{Sin[t]*Cos[t]*Log[Abs[t]],Abs[t]^(0.3)Cos[t]^(0.5)},{t,-Pi, Pi},PlotPoints->100]

ParametricPlot[{Cos[3t]+Sin[4t],Sin[3t]+Cos[4t]},{t,-10,10}]

Squares and Circles

ParametricPlot[{Sin[2t],Cos[t+Tan[2t]]},{t,-2 Pi,2 Pi}]

ParametricPlot[{Cos[10t-Cos[100 t]],Sin[100 t]},{t,-2 Pi,2 Pi},PlotPoints->200]

ParametricPlot[{Cos[t+Cos[100 t]],Cos[t+Sin[100 t]]},{t,-2 Pi,2 Pi},PlotPoints->200]

ParametricPlot[{Sin[Tan[t]],Cos[Tan[t]]},{t,-2 Pi,2 Pi},PlotPoints->50]

Artistic

ParametricPlot[{t-Cot[.5t],Sin[2t]^2-Cos[t]},{t,-30,30},AspectRatio->1,PlotRange->{{-20,20},{-2,2}}]

ParametricPlot[{Sin[t Cos[100 t]],Cos[10t-Sin[100 t]]},{t,-2 Pi,2 Pi},PlotPoints->200]

ParametricPlot[{Sin[10t+Cos[100 t]],Cos[t+Sin[100 t]]},{t,-2 Pi,2 Pi},PlotPoints->200]

ParametricPlot[{1.5Tan[t]-Sec[40t],5Sec[t]-Csc[30t]},{t,-50,50}]

ParametricPlot[{1.5Tan[t]-Sec[40t],5Sec[t]-Csc[30t]},{t,-50,50},PlotPoints->3000]

ParametricPlot[{Cos[Sin[5t^2-4Sin[3t]]] ,Sin[Cos[t^4+3Cos[6t]]]},{t,-50,50},PlotPoints->10]

Surprise!