Here are the indie games that I've purchased and would most recommend to others. Listed alphabetically.
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Bonnie's Bookstore This is a casual word-finding game, but extremely well done. The artwork is excellent, and the game mechanics are well implemented, with continual variations in the shape of the game board, and the regular addition of new special tile types, keeping things fresh. I was initially dubious about this -- it's really not my normal thing, and I wasn't sure if it would hold my attention for long -- but it kept me playing and won me over. Definitely check it out if you enjoy word games.
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Brainpipe Digital Eel are very good at creating games that you might only play in short bursts, but will keep on your hard-drive permanently, meaning that their games are there any time you feel like a quick burst of fun. Brainpipe has you flying through your own mind, avoiding harmful obstacles, and collecting glyphs for extra points. The graphics are neat (if difficult to make sense of in static screenshots), the gameplay is smooth, and the soundtrack is superb, constantly throwing strange little 'memories' out at you. As with most Digital Eel games, things are randomised so that the game never gets old.
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Crimsonland An incredibly addictive top-down shooter. With several modes of play, masses of weapons, power-ups, and 'perks' (special abilities), and some excellent humour, Crimsonland is a must-buy for arcade shooter fans.
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Gravitron 2 Not a Thrust clone (no pendulum action here), however that classic is a good point of reference, and Gravitron 2 is simply the best game of that ilk that I have
ever encountered (and ridiculously cheap as well). If you have any affection whatsoever for this style of game, you must buy this. Admittedly I'm a Thrust fanatic, but this was one of my favourite games of last year.
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Gumboy Crazy Adventures An odd and beautiful game. As Gumboy, roll, jump, float, and swim your way through wonderfully-drawn levels in four different worlds. Each world has a particular goal and style of play that differs from the others. Tricky at times, but a little bit magical. The demo and training levels are completely different to the 'main' levels, which is a bit odd. System requirements are higher than you might expect, so be sure to test the demo out first, and play with the detail options if need be.
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Hamsterball Simply put, this is Marble Madness done to perfection.
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Marble Blast Gold Another marble game, but with very different gameplay. Using mouse-look controls from a behind-the-marble perspective, reach the finish line in the time available, while dealing with all manner of obstacles and power-ups. There's a free version available nowadays via Instant Action, but I have a soft spot for the original (which, of course, has the advantage of not needing to be played in a web browser).
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Oasis Utterly brilliant strategy game. Civilisation played in minutes, rather than hours, with a near-perfect learning curve. I almost didn't buy this, because I thought that I had experienced everything there was to do after playing the demo. I was
so wrong. When I finally did buy it, I don't think I played anything else for several
weeks, and I still have occasional flurries of games, as I try to tick off another campaign on Hard or Insane difficulty. Mastering one difficulty level merely means you are ready to challenge yourself with the next, and every campaign features variations in the rules that create new challenges and require different approaches.
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Weird Worlds - Return to Infinite Space The sequel to Strange Adventure in Infinite Space, but bigger (optionally), better, and much much prettier. "Sail the high sea of stars in your own deep space exploration vessel. Discover exotic star systems; seek out new technologies, artifacts and lifeforms; boldly blow up stuff where no one has blown up stuff before!" Like its predecessor (and like Oasis), this is essentially patience in video-game form. Each game is short, generated randomly, and draws you back for more with the possibility of bettering your own high scores if the metaphorical cards are dealt just so (and, of course, you play them well).
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World of Goo Simply overflowing with charm and general wonderfulness, World of Goo is a physics-based arcade puzzler in which you use your goo balls to create bridges and other structures in order to let the remaining goo balls 'escape' the level. Each new chapter brings new gameplay elements, new music, new types of goo, and new delights. The demo is the first chapter, and if you love that it's a no brainer. If you're not 100% convinced, neither was I, but I went ahead and put down the money on the strength of the reviews I'd seen, and was not disappointed. Things really do take off in the subsequent chapters. Short, but oh-so-very sweet, it really does deserve all the accolades.
I might add some others later -- I have certainly bought and enjoyed other indie games -- but I think the ones mentioned above are my favourites.