I'm using Minecraft Forge version 1.4.7-6.6.0.503 and Railcraft version 6.14.0.0. It works when I launch Minecraft without Railcraft, but it crashes when I add Railcraft.

Could you please post the error log, Perhaps pastebin it too.
Can't work out much without an error to go by.

I'm not certain of the current state of RC on 1.4.7, but 1.4.7 has been around long enough and most mods from 1.4.6 work with it, so there shouldn't be too many breaks with 1.4.7

Post the log and I'm sure Covert will be along to let you know

Please direct support requests to the forums at railcraft.info.

Site looks nice CJ!