A pretty good amount, and it’s not accidental or random:
This study examines self-presentation in online dating profiles using a novel cross-validation technique for establishing accuracy. Eighty online daters rated the accuracy of their online self-presentation. Information about participants’ physical attributes was then collected (height, weight, and age) and compared with their online profile, revealing that deviations tended to be ubiquitous but small in magnitude. Men lied more about their height, and women lied more about their weight, with participants farther from the mean lying more. Participants’ self-ratings of accuracy were significantly correlated with observed accuracy, suggesting that inaccuracies were intentional rather than self-deceptive. Overall, participants reported being the least accurate about their photographs and the most accurate about their relationship information. Deception patterns suggest that participants strategically balanced the deceptive opportunities presented by online self-presentation (e.g., the editability of profiles) with the social constraints of establishing romantic relationships (e.g., the anticipation of future interaction).
Source: “Separating Fact From Fiction: An Examination of Deceptive Self-Presentation in Online Dating Profiles” from Personality and Social Psychology Bulletin
Levitt and Dubner also covered aspects of this in Freakonomics. I think they compared variables listed online to average stats on those same variables in the geographic region (e.g., 20% of the male profiles in the area are saying they make 100K+ but from third party data we know only 2% of the men in the area make that much = fishy.)