1) My favorite way of earning neopoints is by playing Evil Fuzzles from Beyond the Stars.
With just a little practice, you'll be able to earn 1,000 NP each game.
All you have to do is click on the fuzzles that go by, without missing. You'll be able to collect lots of 'in a row' bonuses, which are VERY important.
When you reach a station, it is also very important that you buy the gun upgrades. It's the key to getting all those 'in a row' bonuses. You should also buy that thingy that allows you to see from which direction the fuzzles are coming. When your on levels, say, 8 and beyond, you will really need it. Remember to press b and n to look left and right so you can catch those fuzzles that sneak up on you before they reach you.

You can play it 3 times and if you get good, you'll be able to earn 3,000 NP a day.

2) Another way to get neopoints and/or rare items is to visit these places daily:
Fruit Machine   Tombola   Coltzan's Shrine  Free Omelette  The Snowager
(The Snowager sleeps between 6-7 AM 2-3 PM and 10-11 PM)

3) Feeling lucky? The Wheel of Excitement usually gives out good prizes!

4) Whenever you find something or win something you don't want, sell it! Use the Shop Wizard to look it up and see how much it goes for (ignore the value it gives you when you click on the item itself)

5) ...uh... well, I'm spent. I can't think of any more... please neomail me if you have any tips!