What type of bike do you have?
Small fold-up bikes don't require any kind of special reservation as they are considered as luggage, you just find a place for them with your cases in the luggage areas.
Larger (non standard) bikes such as Tandams or tri-cycles will not be allowed on the train in the same way as regular bikes.
Motorbikes are not allowed on passenger trains, they will have to travel on the motor rail services with cars.
Country by Country Guide
Most trains in the UK will allow bikes on board, just find the carriage with the fold away seats and store your bike there. There is no charge for this but just be aware that you should only really do this during off-peak hours, especially when travelling to/from larger cities.
Eurostar - Since the 1st November 2015 you can no longer book a space for your complete bike and take it onboard, you now have to semi-dismantle it and book it in using the Eurostar registered luggage service. This is a bit of a pain as before it was much more bike friendly, you may want to consider getting the train from London to Dover then a Ferry to Calais, then cycle from the port to the main Calais station (around 2 miles) before continuing your journey.
Luggage cars on most non-Premium trains will carry bikes free of charge. If you can get your bike into a bike bag you can take it on any TGV train, this is also true for non-Premium trains.
Most trains in Belgium will take bikes, although you'll need to purchase a bike card from the station before getting on the train.
Intercity trains have a special luggage carriage that can take bikes, as in Belgium you'll need to pay a supplement at the station to put your bike in here. Premium Thalys trains have no provision for taking complete bicycles, they will allow bikes in bike bags as carry on luggage though.
Most of the local and intercity trains in Germany will take bikes on in the luggage car or in the entrance area to the carriage. However, ICE trains require bikes to be in bike bags.
You can get an idea of what's required in most countries from the above, as a general rule a complete bike can be carried on most local and intercity trains in the luggage car or luggage area of the carriage. On Premium/High Speed services it's more than likely that the bike will have to be stored with other luggage in the luggage areas packed up in a bike bag. If you're in any doubt you can always ask at the local station. We'd recommend that you take a bike bag and practice using it a few times so that your first time packing your bike away isn't 3 minutes before the train arrives at the station.
You can buy bike bags from many bike shops or travel accessory shops, just bear in mind that the one you choose should not exceed 120cm x 90cm.