First, do not start a thread about it here. This is a user-to-user forum. It is not a Bluehost support site. There is no one here who can tell you why your site is down, and there's no one here who can do anything about it. This also applies to sites that have been suspended or terminated. Only Bluehost can tell you why your account has been shut down.
Bluehost now has a video tutorial about what you should do if your site is down (not just suspended or terminated), here. The following is pretty much the same advice:
Visit http://serverstatus.bluehost.com and enter your domain name. If the status indicates that there's a problem on your server, or that there's a more general system problem, you can be sure that Bluehost already knows about the problem and is working to correct it. Contacting Bluehost is not necessary. All you can do is wait.
Second, check to find out whether the site is down for everyone, or just for you. Visit http://downforeveryoneorjustme.com/, plug in your domain name, and click on "just me." If it's just you, you've got some kind of DNS or connection problem. Contact your ISP.
If you can get into the Control Panel for your account, click on the Service Status link at the bottom of the column on the left. If you see red dots, this indicates that there is some sort of problem on the server. Again, Bluehost will already be aware of it. Don't worry about red dots on the disk space indicators at the end of the list. These are not the reason your site is down. When the disk drive gets too crowded, Bluehost will start moving some accounts to a new server.
Ping your domain, and also do a tracert from your PC to your domain. If there's a faulty node somewhere between your location and Orem, Utah, there is nothing Bluehost can do about it. You can either wait for the problem to be resolved, or contact your ISP for assistance.
If you've gone through all these steps and still haven't determined why your site is down, contact Bluehost by phone (888-401-4678) or Live Chat (big blue button on the main bluehost.com page).
Bluehost guarantees network uptime of 99.9%, which still works out to about 9 hours of downtime per year. However, Bluehost does not provide any server uptime guarantee. See this knowledgebase article. If you decide you need greater reliability than what you're experiencing, you can cancel your Bluehost account at any time (for any reason), get a prorated refund, and find another web host. Complaining about downtime in these forums will not accomplish anything, and such threads will be closed and/or deleted.