Preserved Railways & Railway Museums - Some Particular Favourites:

The Bluebell Line
The Watercress Line
The Ffestiniog & Welsh Highland Railways
The Swanage Railway
The Paignton and Dartmouth Steam Railway
The St Louis (Illinois, USA) Transport Museum
The National Railway Museum (York)

General Railway Links:

SeMG: The Southern E-group (specialising in Southern Region Railways).
UK Heritage Railways: Links to preserved railways all over the UK.
Cranleigh Railway: information on the now closed Christ's Hospital to Guildford Line.
LBSCR: The London, Brighton and South Coast Railway
Subterranea Britannica: Disused railway stations. Invaluable for the modeller.

Modelling:

N Gauge Society: If you model in N gauge, you NEED to be a member.
N Gauge Yahoo Group: Yahoo mailing list for N gauge modellers.
Graham Farish: Manufacturer of N-Gauge RTR British outline rolling stock.
Dapol: Manufacturer of some really nice models in both N and OO.
ScaleRail: Our 'local' model railway retailer. Funny little room hidden at the back of a bookshop, but great advice and excellent mail-order service.
Gaugemaster: Manufacturer of some excellent DC & DCC controllers and also a terrific retailer. Well worth a visit.
StationSigns: Superb station nameboards, totems and related signs for ANY station name of your choice. Superb quality, swift delivery and a great price. OO or N gauge.

Other:

Pendon Museum: If you live in the UK and are interested in modelling, you MUST visit Pendon. Stunning.