Volapük was designed back in the 1800s to be a 'world language', but at first glance, it appears to the layman (me) to just be a mixing of Romance languages, English, and maybe High German. Are there any new ideas or concepts that were presented in this conlang, or were all of its rules simply derived from these parent languages?
The Volapük panoply of mood suffixes contains distinctions that were familiar to its audience through classicising education, but I think it fair to say they weren't in the immediate source languages: the optative, jussive, and potential moods as suffixes don't correspond to what German or English or French does morphologically; nor does giving a suffix to the apodosis of conditionals (if... then). In fact, while the optative is Ancient Greek and the jussive is Sanskrit, the potential in Europe is limited to Finnish, and the apodosis suffix seems to be completely made of whole cloth.
I'll add that, as with Esperanto, a lot of the compounding was schematic and not inspired by natural languages; the notorious example of lu- "derogatory prefix" is probably the most obvious (bien 'bee' > lubien 'wasp'; vat 'water' > luvat 'urine').