Glasgow Prestwick Airport station is connected by a footbridge to the terminal on the Ayrshire Coast/Glasgow South Western line.
Perhaps Prestwick's number one selling point as an airport is it's station. Being about 45 minutes from Glasgow Central, it's arguably as convenient as Glasgow International Airport is, although the new GARL will change that. Sadly Prestwick's operator Infratil is not in great financial shape, and with Ryanair operating 99% of the scheduled flights the airport isn't in a great position to agree better terms re: taxes and charges. It feels run down and sadly the station reflects that, it being managed and maintained by the airport rather than ScotRail or NR.
A major selling point is the 50% discount on single tickets to or from anywhere in Scotland for arriving or departing passengers. I don't know how this is subsidised, but it makes for a really tempting offer (Ryanair fares + £3.20 train every 30 minutes from Glasgow). It also has escalators and an enclosed bridge direct to the check-in hall:
A couple of airports not mentioned so far are those in Northern Ireland. I make at least one monthly trip to Northern Ireland, flying with Ryanair from Prestwick to Belfast City (Ryanair's shortest flight anywhere: usually 19 minutes runway to runway!).
Belfast City is right in town, compared with Belfast International about 20 miles away, which can be up to an hour in bad traffic. It's also right next to the A2 Belfast/Bangor road and the Belfast/Bangor railway line, with a stop at Sydenham (apologies for the amateur fake-model-train look I tried to get in Photoshop):
Modern CAF C3K DMUs leave at least every half hour towards Bangor and Belfast. So for me it's £3.20 Glasgow -> Prestwick, between £1 and £10 for the flight, and then £1.60 for the train into Belfast-Botanic. Sadly most passengers arriving or leaving from Belfast City by public transport are directed onto the airport bus, which costs about the same but only serves Donegal Square and Belfast-Europa Buscentre, at Great Victoria Street station.
Sydenham station is connected by a rather unappealing footbridge over the A2 to the disused airport entrance next to the old passenger terminal (now a freight and cargo facility). The new terminal, built less than a decade ago is about half a mile further north along the A2, but a free shuttle operates on request between the terminal and a shelter inside the old gates. While waiting for the bus you get to admire the inside of the old security checkpoint that welcomed you to Northern Ireland!
That banner welcoming you to Northern Ireland is so old, it's offered by Jersey European, an airline that's now twice changed its name (although which still serves the airport).
Planning permission is currently being sought for a new sports stadium across the A2 and railway tracks from the new terminal building. Part of the planning application has alluded to a new railway halt that would be next to the stadium, and directly across the dual carriageway from the terminal building, and it also suggested an enclosed footbridge could be constructed. That application was made completely independently of Belfast City Airport, however, and I don't know whether they would be at all interested in contributing to the cost of that project.
NI has two other airports: Belfast International has the Lisburn/Antrim railway line that passes close to the airport perimeter, but no passenger services use it anymore; a more direct route between Belfast and Antrim (instead of going south via Lisburn) was re-opened with the Mossley Viaduct more than ten years ago.
1982 NI Railways map (Belfast International Airport is close to stations numbered 32 & 33) and
2005 NIR map (pdf).
A circular Belfast - Belfast train service via a new airport station and Antrim has been discussed, but right now money is being concentrated on upgrading the remainder of the Londonderry line and replacing the 450 'Castle' (aka 'Cattle') class trains on the Belfast / Larne line. You'd still face the decision about whether to build a spur into the International Airport or having a bus shuttle connecting the terminal with the station; it's not really close enough to walk.
The very scenic but until recently slow, unreliable and bumpy Belfast / Londonderry railway line passes by the perimeter of City of Derry airport. However it's on the wrong side of the airport for the terminal, and there is unlikely to be the passenger numbers from LDY to justify a station on that line.
