What is the furthest you have seen on a clear day with the naked eye (objects or clouds on Earth)?  Back in 2009 during mid June, I took a photo of an orphan anvil in the twilight sky from ground level. When I checked the radar to see where the shower could have been, it turned out it was over Dumfries and Galloway about 120 or so miles away. I have also seen anvils from my location from cells just off the east coast of Ireland.

Here's a website of what you can see and their distances from high points across the globe including the UK

http://viewfinderpanoramas.org/panoramas.html

Aside from being on a plane (which is kind of cheating):

Denali from Anchorage, visible as a faint outline on the horizon looking north (roughly).

In the UK, 7 or so miles from the top of the Shard. Unfortunately it was quite a humid day; one of those crisp, sparkling days would have afforded a view 3 or 4 times as far.

(Non-zoomed)

(Full zoom)

If conditions are decent enough at this end, I could make out the colours on rows of houses on the French coast when viewed from my front garden with the naked eye (making sure that is the only part of me that is naked!).

With a long zoom camera, I might be able to spot the whites on a Frenchman's eyes as he leave his favourite bagel shop.

From the hills of Purbeck, we once marvelled at the view West on a cool, sunny day, with very clear vista to Weymouth and Portland, the sunlight twinkling on buildings beyond presumably around Lyme Bay, and yet further to an indistinct dark line which we debated could be the Devon coast/ hills although we also wondered if it might be haze/ pollutants. That's about 80k (50 miles).

Ah yes, the classic one was that you can read the time on the clock of the hôtel de ville in Calais from the tops of the cliffs in Dover - sadly the only time I've been up there was when it was chucking it down on a school trip many years ago!

You can see the white cliffs from the harbour in Calais though, I remember being astonished to see them from the window of the Pride of Burgandy before we'd even set off from Calais one early summer day in the 90s.

That website is excellent - could spend hours looking at that. :-)

When I was on the Monadh Liath above Newtonmore a couple of years back I could see Ben Klibreck (80 miles) and Ben Hope (90 miles).  But pretty sure I have seen further on occasion

I saw the sun last month, does this count?  (About 93 million miles or so)

Seriously though that link Kevin posted is great. I know I have seen for dozens of miles from the Scottish peaks at various times and on a clear day it really is amazing how far you can see.

You can often see Mount Rainier from Seattle as a slightly ghostly backdrop as I did in 1993

I think it's about 60-70 miles

What a great thread.

As far as the moon when out in the daytime.

That's an amazing sight and you're right- it's almost a spectral shadow. I reckon it's a bit closer than 60- less than 50 miles as the light flies.At such a distance, it does look huge.

The link I provided gives it about 60 miles

Yes, I can see you're right- so much for my attempt at estimating it from a map. It looked so tall at that distance, I couldn't quite believe it. It does look huge in that picture.

I know a clairvoyant who claims to see far into the future.

If I am being serious......

On a clear day with arctic North Westerlies, it is possible to see the Wicklow mountains in Eire from Sea Level in Mid Wales ( Aberystwyth).. ..

Didn't believe it till In took aa bearing... Now seen it 3 or 4 times in the last few years.. !!!!

Presumably, it's  possible when you see a cloud near the horizon , to estimate how many miles away is the place where that cloud is directly overhead? I assume you can use some kind of simple mathematical formula based on the type of cloud and therefore estimating it's height? 

It is.

1.17 times the square root of your height of eye = Distance to the horizon in nautical miles 

Further info see here 

http://www.boatsafe.com/nauticalknowhow/distance.htm

You can see the London skyline (notably The Shard, BT Tower and Canary Wharf) from the top of Caesar's Camp near Farnborough. Google Maps gives the distance as a little over 38 miles to Canary Wharf.

As Seville3332 says, you can also see the contrails of aircraft over huge distances, especially close to sunset when they catch the light. I've watched planes heading off to the west from my upstairs window and using flight tracking sites worked out that I can still see them when they reach mid Wales from here in Hampshire - roughly 125 miles.

Further afield, I've (just about) seen Kilimanjaro above the clouds from the upper slopes of Mt Kenya (almost exactly 200 miles). Very tall mountains with flat plains in between.