Yes, they are. Source: scientific consensus.
Consider the following phylogeny of the primates: 
If we choose to exclude all non-simian primates from monkeyhood, you still cannot create a scientifically valid monophyletic grouping of monkeys that doesn't include the apes (hominoidae) without excluding the new world monkeys (platyrrhini). This is because the two main groups of monkeys, the platyrrhini and the catarrhini, split before the catarrhine simians split between the tailless old world monkeys (hominoidae) and the tailed old world monkeys (cercopithecoidae). If you told any primatologist, any biologist in general, any person on the street even, that howler monkeys and spider monkeys are not actually monkeys, you would rightly face raucous laughter and bemused derision.
At this point, we have to address the elephant in the room that is the arbitrary delineation between monkey and ape based on tailedness. If we are to divide the apes from the monkeys solely on the basis of appearance, then why not cleave the hyraxes from their elephant and manatee cousins and graft them onto the rodents they so closely resemble? Why not call tuataras lizards while denying snakes the same title? Why not just call dolphins a kind of shark, since they're both sharkish in shape and lack the scales of other fish? Why not just say birds aren't dinosaurs because they don't look like a brontosaurus? Because it's unscientific derangement, that's why. Paraphyletic groupings based on arbitrary physical markers is as against scientific consensus as it gets.
Formerly Chucksville.