I am flying from Heathrow to Toronto via Washington with checked-in bags. I know I cannot check my bags all the way through and will have to pick them up at US customs, but where do I check them in again on the Washington to Toronto leg of my journey? It is a completely different airline with no affiliation (Virgin Atlantic and Porter). Do I have to go out to the check-in desks again?
If you're flying on a single ticket, you can be 98% sure that your bags will get tagged all the way through to Toronto.
In Washington you will need to pick them up from the carousel and carry them through the customs check, but you can then drop them at a bag drop immediately after customs; you don't need to get new tags for them.
If your flights are on different tickets, you will generally need to seek out a check-in desk/kiosk after clearing customs to get your bags checked in and tagged for the second flight.
Note that single tickets can often be issued perfectly well for a combination of airlines that you wouldn't recognize as "affiliated" in any way. Practically all full-service airlines -- as well as many that otherwise walk and quack like low-cost carriers -- will happily interline with each other even if they don't market their services together. (If you're an airline, it makes business sense to earn a profit on half of the passenger's journey rather than risk him going to a competitor because you refuse to play with the airline he wants to use for the other half).
Thanks to all of you for your comments. For anyone who may need to know this for future travels, I did have to go out to the check-in desks again and go through security at Washington (you can drop your bags off only if you are on a star alliance flight). You need to leave yourself a lot of time to go through IAD customs (early afternoon appears to be particularly busy). I chose this airport for transfer, as it was supposed to be so much better now with passport direct kiosks. There were lines and lines of automated kiosks, but they weren't being used (on either leg of the journey) so no improvement there. Also, only 3 visitor desks were being operated when there must have been over 1000 people in the visitor queue. I queued for 3 hours and I was one of the lucky ones! Literally just made my connecting flight back to London!
Billy Bishop airport is a breeze though - I'd highly recommend it!