This post should provide you with a better idea of what types of games exist and which ones are possible in Flash.
There are also some strong reasons for not choosing Flash as your development platform. It's important to know them as well, before you get started and encounter unpleasant surprises.

Performance
Macromedia spent thousands of hours making the required Flash plug-in for the Web as as possible so that the maximum number of people could download it easily. But that required some and the major one was performance. Flash underperforms virtually all other game-development platforms speed of code execution and graphics rendering. On the other side of the fence, game-development like Macromedia Director and WildTangent perform very well—but have enormous plug-ins. As a result, few people can view such content without being forced to download the plug-in in addition to the game.

Lack of 3D support
Flash doesn't provide native support for real 3D engines or for any sort of texture mapping (the act of applying an image to a 3D polygon).

Lack of operating-system integration
When you run your game as a Projector file, Flash cannot easily talk to the local operating system to do things like browse files on the hard drive. (But this type of possible with the use of third-party software such as Northern Codeworks' SWF Studio, available at http://www.northcode.com.) Most of the developers who choose Flash as their game-creation tool do so because they want their games be available to many people easily on the Internet. If the intention is to have the game available offline on ROM, then Flash is still a choice—just not necessarily the best choice.

Infeasible Game Features
It is much easier to talk about things Flash cannot do easily than to discuss everything it can do. Here I'll on some things that are very difficult to achieve in Flash, or that aren't feasible for another reason. I don't to say anything is impossible with Flash, because there are so many creative people out there with dozens tricks to make the seemingly impossible possible.

3D rendering with texture mapping
Many people have created 3D engines with ActionScript. A 3D engine is code that can take 3D coordinates map them onto your screen. While these engines actually manipulate coordinates in 3D space and then map
them correctly back onto a 2D screen, there are three major limitations:

Texture mapping
You cannot map textures (bitmap images) onto an object in Flash. As I have already mentioned, many people make creative attempts to get around program obstacles. People have successfully done very simple mapping onto flat surfaces.

Z-sorting
This refers to the order in which objects appear in front of other objects. In real 3D rendering games, the sorting order is not limited to whole objects, but can actually pierce surfaces of objects (if two things happen to be moving through each other). Flash is limited to sorting at the movie-clip level.

Speed
Three-dimensional engines written in Flash can typically handle only simple shapes, and they retain frame rate close to the frame rate of your SWF. Complex scenes are often very CPU-intensive, and the rate can suffer as a result.

Real-time multiplayer games
Creating this kind of game is certainly possible, but for many reasons it is not easy to accomplish. One of the
main factors is the nature of these games. Due to network latency, it would be very difficult, if even possible,
create a real-time multiplayer game like, say, Mortal Kombat. However, some real-time multiplayer games
lack interaction between players, such as a scavenger hunt, might be more feasible.

Intense real-time calculation
I know this sounds like a vague limitation. But when you're creating a game, it is important (although admittedly difficult) to think ahead and try to guess how intense the calculations are going to be. For a game that has dozens of enemies—who all think for themselves and constantly run around trying to decide what to do next—is an excellent candidate to bog down the computer processor! You'll have to do a lot of testing and experimenting to determine exactly how many of these enemies the computer can handle and perform well.

But...

Web deployment
Since Flash files are designed to be viewed in Web pages, Flash is a good choice if you want your game to be available on the Internet.

Small file size
Flash makes use of vector graphics and compressed sound files, so a Flash game's final file size can be exponentially smaller than those of games developed on other platforms.

Plug-in penetration
The plug-in that's required for viewing Flash files in a Web page comes with all major browsers. More than 98 percent of people on the Internet worldwide can view Flash content. The exact penetration for each version of the plug-in is listed on the Macromedia Web site (go to
www.macromedia.com/software/player_census).

Server-side integration
Flash games can talk to the server seamlessly. Using Flash's built-in features, can communicate with server-side applications that make chats, multiplayer games, and high score lists possible.

File sharing
Between programmer and graphic artists/designers, and between users. With Flash, programmers and artists can collaborate using the same files. This is rare in game development. Users spread a good game a lot over the internet. So, provide embedded links to your home!

Ease of use
Perhaps one of the most attractive reasons for choosing Flash is that you can learn the and start creating games in a very short time. With other languages, it could take years!