You can copy modifiers from one object to other objects with CtrlL> Make links > Modifiers, or the Copy attributes addon.
However, is it possible to apply modifiers to many objects at once?
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One very easy way to do this is to use the Convert To command:
If you have curve objects that need to stay curves, then use Convert to Curve
ALTC -> Convert to -> Curve from Mesh/Text
If you have mesh objects that need to stay meshes, then use Convert to Mesh
ALTC -> Convert to -> Mesh from Curve/Meta/Surf/Text
This will automatically apply all modifiers at once:
Blender 2.8x comes with the add-on "Modifier Tools".
The add-on ads four buttons in the top area of the Modifier tab and the entry "Apply All Modifiers" in the menu under "Object" - "Apply".
In addition to applying and deleting the entire modifier stack, you can also disable it in the Viewport (Viewport Vis) and collapse/expand all modifiers with the press of one button (Toggle Stack).