It's not recommended to use java code inside jsp. You should try to avoid it.
The approach that needs to be followed in your case, is to first set the Arraylist as an attribute in the servlet that is calling the jsp page.
Servlet Code
ArrayList databaseArrayList = new ArrayList();
...
request.setAttribute("databaseList", databaseArrayList);
Then, in the JSP code, use jstl to iterate through the values of the list to populate the select options.
JSP Code
<select name="database1">
<c:forEach items="${databaseList}" var="databaseValue">
<option value="${databaseValue}">
${databaseValue}
</option>
</c:forEach>
</select>
I've written an article for looping over HashMap and ArrayList in JSP
