The game type that most people try to do initially, as well as the one that burns out the most developers, is the completed game type. These games are polished into a shining gem from a muddy piece of coal drudged from the developer's mind. While it certainly has a positive effect on one's reputation to release a good game with significant depth and thought put into it, there are a number of problems with this method of development.

1. Feedback is not immediate. Players will not pick up your game and play it before it is released, meaning that you can put in a terrible gameplay system that ruins the game without ever realizing it. This slow turnaround can severely hurt a game that has a much longer development cycle than a few hours/days. The best way to fix this is to get some new testers each time you want to get some feeback on your continued progress. While not as widespread as public testing/release, it definitely saves some of the surprise of the full game for the general populace.
2. The developers can burn themselves out. We're talking a development time of anywhere from two to five years. That's a lot of time, and developers can feel like they aren't making any progress. This is especially prevalent at the end of a project, as most of the important stuff has been finished (engine, art, etc) and it's mostly gameplay tweaks and polish.
3. High risk of market change. As the game takes so long to make, the market may have moved on from the original concept as a good game by the time you are finished with your game. This means nobody will play your game. While this is very much less of an issue with the indie game community than it is with mainstream games, it does happen.

There are some perks, though. As the development cycle is so long, you can (with good feedback) create a lengthy and highly-polished game. You are also free to experiment within your game a little, changing around design principles without destroying the game itself. Cave Story is the epitome of a finely tuned, polished, and released indie game in this category, but there are many others (such as Iji)

Your other potential way of making your game is creating a bunch of conceptual games within a short period. You can either focus on milling through ideas, or do a bunch of conceptual games and then take the lessons learned from one and apply it to a longer game. The biggest difference between this category and the more polished one is that a concept developer creates concept games constantly, rather than take some and make them into full games. There are problems with this, though.

1. Games are not polished at all. They are often lacking in graphics, sound, or even gameplay, and players will definitely let you know about your game being a waste of their time. This can lead to extremely negative feedback and make players no longer play your games. On the flip side, players may love your games despite the shortcomings and rocket you into stardom.
2. No time to complete everything. This sort of falls under polished, but where polishing is finishing and then tweaking, conceptual designers don't even have that luxury. They design and move on, and if it fails, oh well. A lot of games are made missing features that were considered because of time constraints.
3. People may consider you a nobody. Since you never put out a finished game, people may eventually get bored of your output and come to the conclusion that you can't do a finished game because you suck. Alternatively, they may think you have the attention span of a goldfish. More negative feeback results from this!
   

As you can probably tell, negative feeback is the biggest problem with conceptual game design and creation. Some players absolutely hate it and will badmouth you for developing games like that, where it is rare to see someone belittle a developer for taking their time to polish a game. However, this extremely quick turnover of games and feedback lets you prototype future games very quickly and build a reputation on experiences you made in 3 hours. The most notable conceptual developer is cactus, whose output is almsot terrifying in its sheer volume.

In the end, it's really a personal decision which path you want to go down. Neither is right and neither is wrong. They are merely two sides of the same coin. You can even strike a balance if you want, such as doing rapid prototyping until a good game is found, and then expanding it into a full product. No matter which path you go, though, remember one thing: the player is law. Make your games to please, excite, or engage the player, and you will never be far off base from a good design.

For more coverage on indie games and the scene, keep an eye out for Indie Showcase at the same bat time, same bat channel. Also check out Freeware Friday and our indie category for some excellent freeware games and indie news, respectively.