I had the same concern and asked my family doctor. He showed me the recommendations from the American College of Chest Physicians.
Below you can find an extract:
VTE = Venous Thromboembolism (includes Pulmonary Embolism, Deep Vein Thrombosis)
GCS = Graduated compression stockings
6.0 Persons Traveling Long-Distance
6.1.1. For long-distance travelers at increased risk of VTE (including previous VTE, recent surgery or trauma, active malignancy, pregnancy,
estrogen use, advanced age, limited mobility, severe obesity, or known
thrombophilic disorder), we suggest frequent ambulation, calf muscle
exercise, or sitting in an aisle seat if feasible (Grade 2C).
6.1.2. For long-distance travelers at increased risk of VTE (including previous VTE, recent surgery or trauma, active malignancy, pregnancy,
estrogen use, advanced age, limited mobility, severe obesity, or known
thrombophilic disorder), we suggest use of properly fitted, below-knee
GCS providing 15 to 30 mm Hg of pressure at the ankle during travel
(Grade 2C). For all other long-distance travelers, we suggest against
the use of GCS (Grade 2C).
6.1.3. For long-distance travelers, we suggest against the use of aspirin or anticoagulants to prevent VTE (Grade 2C).
You can find the complete version here: http://www.chestnet.org/Guidelines-and-Resources/CHEST-Guideline-Topic-Areas/Pulmonary-Vascular
Guyatt GH, Akl EA, Crowther M, Gutterman DD, Schuünemann HJ. Chest. 2012;141(2_suppl):7S-47S. doi:10.1378/chest.1412S3.
P.S (if like me, you are wondering what the grading means): the grading corresponds to the level of "evidence" for this recommendation. Grade 2C means that randomized trials are still missing, and that this decision was made by balancing the risk and benefits of the intervention. This website gives a good explanation of the grade system: http://www.medicographia.com/2011/12/rating-the-quality-of-evidence-and-the-strength-of-recommendationsthe-new-grade-system-in-venous-disease/