We recently flew from Colorado Springs to Edinburgh, and four of our five flights were delayed/cancelled. We did check in online, so airport check-in went smoothly, and we did opt to check our bags.
Our outbound flight from Chicago to Dulles was delayed due to mechanical issues, at which point we were moved to another plane. Our flight to Edinburgh from Dulles had to be held for us (there were around 60 of us on the ORD-IAD flight that were booked on the IAD-EDI flight), but once we had been in the air about 1 1/2 hours, the plane was turned back to IAD due to mechanical issues, landing back at IAD at 3:30 AM. The flight was cancelled and rescheduled for 9:00 that night. The airline couldn't get us into hotel rooms at that point (leaving us to attempt sleeping on benches), but thankfully we had United Club passes, so once it opened we were able to take turns napping in the much more cushy armchairs. We eventually got on our flight, and landed in Edinburgh a day later than planned.
On our return trip, our flight from Heathrow was delayed by about 2 hours (due to a medical emergency on the previous flight on the plane we were using), which would have caused us to miss our connecting flight in Denver, so I quickly rebooked us on a later flight out of DIA. When we landed at DIA, there were additional delays due to weather, and we ended up spending 5 hours there (65 miles from home).
As I mentioned, we did check our (carryon) luggage both ways, and I'm glad we did, because between running for tight connections and being stuck in airports, it was one less thing to deal with. I just had my daypack, which was easily managed, and since we knew to carry our medications and overnight items with us, it was no big deal to be without our bags. They were waiting for us in Edinburgh and at DIA, no problem. With the new electronic tracking on the bags, there's far less likelihood they won't arrive at your destination, let alone be lost forever.