Denver International Airport: The sensible car-free choice is a prebooked shared mountain shuttle (for example, Summit Express) direct to Breckenridge lodgings or the Breckenridge Station area. Allow roughly 2.5–3.5 hours in normal conditions and about $65–$129 one way; I-70 and the Highway 9 approach can turn a winter transfer into a much longer one. Renting a car is worthwhile only if you plan to explore beyond Summit County; do not assume it will save time on a storm or holiday Friday.
Eagle County Regional Airport: EGE is closer on the map but has far fewer flights. A rental car is usually the practical transfer: roughly 1.5–2 hours via I-70 and Highway 9, conditions permitting. Some prebooked mountain shuttles serve Eagle-to-Summit routes, but confirm the seasonal schedule before buying the flight; this is not a turn-up-and-go transit connection.
Colorado Springs Airport: Use a rental car; expect roughly 2.5–3.5 hours via US-24/Highway 9 or I-70/Highway 9 depending on conditions. It is an alternative only when the airfare works dramatically better than Denver’s: there is no comparably straightforward, frequent public airport transfer to Breckenridge.