AFAIK most Americans call a saddle a seat, whereas in the UK it's invariably a saddle (we'll find out when they wake up!).
There's also 'pavement' - in the UK the pavement is what Americans call the sidewalk, whereas in the US I think it's the road.
You get slagged in the UK if you refer to a mudguard as a fender, but I think 'fender' is a far more elegant word. 'Mudguard' reminds me of when the French actress Leslie Caron was on the Parkinson chat show years and years ago and bemoaned the fact that German was such a crude, unromantic language compared to French - as an example she said the literal translation of 'nipple' in German is 'breast wart'. Don't know what it is in French but 'mudguard' is a bit like that compared to 'fender'.
It's the other way around, I think, with 'cycling' and 'biking' - I far prefer 'cycling'. Also, in the UK a 'biker' is a motorcyclist, never a pedal cyclist, although I think that might be the same in the US.
In the UK a bike shop tends to be referred to as a 'LBS' - local bike shop - whereas Americans use the term 'cyclery', which I think is a lovely word. Of course, 'shop' in the UK is only somewhere you buy and sell stuff, whereas in the US it's also an abbreviation for workshop - where stuff is fabricated or worked on - although I suppose a bike shop counts as both.
'Tyre' and 'tire' is interesting - it's not like other English/American spellings. Apparently the story is that 'tire' is an abbreviation of 'attire' - what wheels were covered with - in the early days, metal bands, just like horses wear shoes to protect their hooves. When the rubber tire was invented, in the UK the spelling was altered to 'tyre' to make the distinction between it and metal bands, but in the US the original English spelling - 'tire' - was retained.
'Aluminum' by all accounts was a US typo for 'aluminium', but by the time the error was discovered it was too late to change it so the incorrect spelling stuck.
Even quote marks are different, btw - in the UK we use one where in the US they use two, then when there's a quote within a quote we use two where in the US they use one (as if it matters!).