For decades large corporations as well as labor placement services have maintained extensive yet static resume databanks. Online professional networks like LinkedIn have taken these resume databanks to a dynamic, constantly updated and massive scale professional profile dataset spanning career records from hundreds of industries, millions of companies and hundreds of millions of people worldwide. Using this professional profile dataset, this paper attempts to model profiles of individuals as a sequence of positions held by them as a time-series of nodes, each of which represents one particular position or job experience in the individual's career trajectory. These career trajectory models can be employed in various utility applications including career trajectory planning for students in schools & universities using knowledge inferred from real world career outcomes. They can also be employed for decoding sequences to uncover paths leading to certain professional milestones from a user's current professional status. We deploy the proposed technique to ascertain professional similarity between two individuals by developing a similarity measure SimCareers (Similar Career Paths). The measure employs sequence alignment between two career trajectories to quantify professional similarity between career paths. To the best of our knowledge, SimCareers is the first framework to model professional similarity between two people taking account their career trajectory information. We posit, that using the temporal and structural features of a career trajectory for modeling profile similarity is a far more superior approach than using similarity measures on semi-structured attribute representation of a profile for this application. We validate our hypothesis by extensive quantitative evaluations on a gold dataset of similar profiles generated from recruiting activity logs from actual recruiters using LinkedIn. In addition, we show significant improvements in engagement by running an A/B test on a real-world application called Similar Profiles on LinkedIn, world's largest online professional network.