While I love @Lucas Wojciechowski's answer, I'd also like to answer this from a different direction, as OP is asking about the distance covered in a single day.
I think here the estimate of roughly 20-30 km per day (13-20 miles) is a reasonable base-line assumption given:
- you know you'll be on decent trails without excessive elevation
- you won't waste time on navigation (because of obvious landmarks or good trail signage)
- your goal is to cover ground (i.e. no hours spent fishing, landscape painting, sightseeing, etc...)
This will be sustainable for longer multi-day treks even with reasonable pack weight (15-25kg) and with mediocre stamina & training. Also this assumes that you need to spend time to break camp in the morning, setup camp at night, spend time cooking, collecting/purifying water, getting stuff out of and into your backpacks - in short on an 8-10 hour day you'll hardly do 8-10 hours of actual walking.
--> But, all of this considered, in my experience (of many months and hundreds of kilometers of treks) the 20-30 km/day can be a reasonable assumption to base any route planning on if you want to plan a trek on a well-mainained long-distance hiking trail (e.g. Kungsleden, Appalachian, CDT, Camino de Santiago, ...).
If you ever go off-trail, then all bets are off: as Lucas outlined in his answer, depending on various factors your speed can slow to a crawl. In such situations you either need good beta on the planned route (e.g. from locals, a good guide book, etc.) or you need to plan with very conservative speeds, to ensure they will be sustainable for you and your group.
 This is especially true because over multi-day hikes any daily deviations tend to even out over multiple days.