1.Do applications using ejb's always have to be deployed as EAR ?
No.
The EJB module is assembled into a JAR, lets call it myapp-ejb.jar as a naming convention.
This contains the EJB code as well as the deployment descriptor file called ejb-jar.xml in EJB 2.x. In EJB 3.0, the code itself contains the annotations required for the server to understand for deployment, so the deployment descriptors are optional. The deployment descriptor/annotations cover basic stuff needed for EJB deployment like the JNDI, DataSource look up etc.
A collection of multiple EJB modules and other Web modules (war) together make up an EAR. As @Isaac pointed out, an EAR doesn't have to include any WAR file in it. The only condition for an EAR file is to contain at least one J2EE module of any kind.
The EAR needs a META-INF/application.xml
which lists all the EJB jars and wars present in the EAR. So you go for an EAR when you have multiple EJB modules which is usually the case, hence the usual deployment is of an EAR.
An example of this file is shown below taken from http://download.oracle.com/docs/cd/B32110_01/web.1013/b28221/undejdev003.htm. This is a good article for you to read.
<application>
<display-name>master-application</display-name>
<module>
<ejb>ejb1.jar</ejb>
</module>
<module>
<ejb>ejb2.jar</ejb>
</module>
<module>
<java>appclient.jar</java>
</module>
<module>
<web>
<web-uri>clientweb.war</web-uri>
<context-root>webapp</context-root>
</web>
</module>
<module>
<ejb>ejb3.jar</ejb>
</module>
2.Can applications containing EJB's be deployed just like other other java
web projects using ECLIPSE and without
using ANT
Yes, once an EAR/JAR is assembled it can be deployed into a server (via Eclipse if you wish).
Ant is a build tool which has nothing to do with the actual deploying of the EJB code. It is used to compile and assemble the JAR - which can be done from Eclipse as well.
Here is a tutorial which does just that.
Further Reading
Packaging Applications
Packaging EJB3 Applications