How can I help my trains move up hills?

Quite a lot of momentum is lost when my trains go uphill. However, when first launching OpenTTD, the initial screen shows trains that lose no speed while ascending. Aside from toggling some setting to make the "physics" unrealistic, is there something I can be doing to my trains to minimize the amount of impact they suffer from going up an incline?

If you really need to climb the hill (and can't go through or around it) then the ways to get a train to maintain speed as much as possible up-hill are:

• Make the train weight less (with less carriages, usually).

• More horsepower. Fit a stronger engine, or consider using multiple engines per train.

• Make the incline shallower. Since all inclines are the same angle of slope, you can only do this by "spreading out" the hill. Ideally the train should only have one upwards hill section under it's length.
  Here's an example of what I mean that I just threw together, notice how the train is 5 squares long and the hills are 4-squares separated:
  

All these assume you have realistic train acceleration enabled (and you really should - the original acceleration model is really slow on all hills, where realistic attempts to simulate momentum).

Also, if you want to tweak things a little bit in to your favour, you can change the calculated steepness of slopes if need be.

First, you could make a tunnel through the hill if really need it to be fast, and the faster that it's going when it hits the hill, the faster that it will get over the hill, and the less that it will slow down.

The most direct answer is that you should buy trains with higher horsepower so that they can power through it better, and the fewer cars that are hooked up the less that it has to pull. If you're having trouble finding powerful enough trains, try electric rails, those have a lot higher power than most diesel or steam trains.