It only takes a one time fee of $25 for a developer to start putting apps on the market. No hoops to jump through. $25 and you can publish as many applications as you want, instantly. No waiting, no queues, no approval process, nada.
However, there have been a few cases of malicious applications. When these problems arise, Google usually pulls them from the Market (and from user's phones). It doesn't happen very often.
Android was designed to to keep yourself protected: all applications have to ask for "permissions" to do certain things: make calls, read contact data, access the internet, etc. Read the permissions before you install an application. Make sure you know and understand what it is going to be doing. Does it seem to have a dubious "permission" that it asks for access to? However, at the same time: don't berate the developer because of certain permissions. Some ads ran in apps require at least the internet permission and sometimes some other ones (about the phone state, I believe). Be sure to have a thorough understanding of why a developer would need certain permissions. Most importantly, read what other people are saying about the application in the market. Read some of the comments (although beware that the comments on the Android market are the same level as Youtube in terms of quality) and see what the app's rating is. Have you heard of the app before? Has a blog mentioned or reviewed it?
Worse case scenario: if you aren't rooted, then no single application should be able to damage your phone as every application is sandboxed from each other (technically, each developer's set of applications are sandboxed from each other. Apps signed by the same developer key can have access to other apps signed by the same developer). They could potentially steal your data, depending on the amount of permissions the application is given. The rarest scenario I can think of is if an application uses an exploit to enable root access on your phone and then does something malicious (e.g., delete everything).