As you may know, I own a Canon EOS 350D. It came with the following two lenses: EF-S 18-55 and EF 55-200.
Mostly I`m absolutely satisfied with my equipment, but sometimes 200mm isn`t enough. Last weekend I was in Switzerland on an airshow and I took many pictures of the planes. But mostly they are too far away.
I have this problem also every time I`m spotting on the airport.

So I thought it would be enough to get Photoshop Elements and try to make them better..
But next problem is, if I cut out the part of the picture showing the aircraft, it gets grainy. There`s a lot you can do with Elements, but it`s not enough to make these pictures looking real good.

So I think my 200mm lens isn`t good enough. I thought about buying the 100-400 L IS, but this time it`s too expensive.

What else can I do to get better pictures? I had a lot of fun taking them, but now it`s sad to see that they aren`t that good as you wished they would be..

Depends on your budget.
The 100-400 for sure will solve your problems but it is very expensive. I really like primes so I'd take a used Canon 300/4L (non IS version, the older one)which goes about 600 euros. In the future you caould also add a 1,4x to obtain a 420/5.6L lens with minimal Image Quality loss.
For this price you have superb image quality. If you want a Zoom also the new 70-300 4/5,6 IS USM seems a nice lens in the 500 euro range.

If you want to stay on the cheap side:
75-300 4/5,6 USM II (or the new III)
sigma 70-300 APO (red ring)
tokina 80-400 AT-X (II)

but they are not so excellent at the long end. You'll have to stop down them.

hope this help

If you're on a budget find a good used copy of the Canon 100-300mm USM lens, it's been around since the early 90's and is still regarded as a pretty good lens. Plus it has the ultrasonic motor for fast and quiet focusing, I have one and have been using it since 1992.