You could use an Advanced Filter. Put the column headers in a separate part of the sheet (or a different sheet altogether). Under those column headers, put the criteria you're looking for in each column. Then name that range (including the headers) something like "Criteria". Then the macro becomes:
Sub Macro1()
Sheets("Sheet1").Range("A1").CurrentRegion.AdvancedFilter xlFilterInPlace, Range("Criteria")
End Sub
As a follow up to my comment below, to have the VBA create the criteria range behind the scenes:
Sub Macro1()
'Code up here that defines the criteria
Application.ScreenUpdating = False
Application.DisplayAlerts = False
With Sheets.Add
'Create the advanced filter criteria range
.Range("A1") = "HeaderA"
.Range("B1") = "HeaderB"
.Range("C1") = "HeaderC"
.Range("A2") = criteria1Name
.Range("B2") = criteria2Name
.Range("C2") = criteria3Name
'Alternately, to save space:
'.Range("A1:C1").Value = Array("HeaderA", "HeaderB", "HeaderC")
'.Range("A2:C2").Value = Array(criteria1Name, criteria2Name, criteria3Name)
'Then perform the advanced filter
Sheets("Sheet1").Range("A1").CurrentRegion.AdvancedFilter xlFilterInPlace, .Range("A1:C2")
'Remove behind the scenes sheet now that the filter is completed
.Delete
End With
Application.ScreenUpdating = True
Application.DisplayAlerts = True
End Sub