<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\cal B}(H)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">B</mi> </mrow> <mo stretchy="false">(</mo> <mi>H</mi> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> denote the algebra of all bounded linear operators on a separable Hilbert space, equipped with the norm topology. A property is called typical if the set of operators fulfilling the property is co-meager. We show that having non-empty continuous spectrum is a typical property and that the set of operators with empty continuous spectrum is dense in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\cal B}(H)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">B</mi> </mrow> <mo stretchy="false">(</mo> <mi>H</mi> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation>. In addition, we show that the set of operators with empty point spectrum is nowhere dense. Moreover, we characterize the closure of the set of operators whose spectrum and point spectrum coincide.</p>