The 2nd one is using generics which came in with Java 1.5. It will reduce the number of casts in your code & can help you catch errors at compiletime instead of runtime. That said, it depends on what you are coding. A quick & dirty map to hold a few objects of various types doesn't need generics. But if the map is holding objects all descending from a type other than Object, it can be worth it.
The prior poster is incorrect about the array in a map. An array is actually an object, so it is a valid value.
Map<String,Object> map = new HashMap<String,Object>();
map.put("one",1); // autoboxed to an object
map.put("two", new int[]{1,2} ); // array of ints is an object
map.put("three","hello"); // string is an object
Also, since HashMap is an object, it can also be a value in a HashMap.