1. Arraylist is not synchronized while vector is.
2. Arraylist has no default size while vector has a default 
size of 10.

Arraylist is not synchronized where as Vector is
synchronized.   
No default size for Arraylist where as Vector is having a
default size of 10.

i would like to add a new point to above answers.
we can specify the increment size with the vector and with 
array list we cannot

ArrayList is non synchronized.Vector is
synchronized.ArrayList is very fast because non
synchronized.we can specify the increment size with the
vector and with arrayList we cannot

Hi...
ArrayList is not synchronized(not Thread-safe)but Vector is 
Synchronized(Thread-safe)
ArrayList gives u better performance than Vector

I am adding some more points to the above answers.

Array list and Vector have one in common. They both 
implement Random Access.
It is possible to provide synchronization using Array List 
by using the utility methods in Collection.

for addition of 3rd answer incresing capacity in vector 
using with ensureCapacity(int x) method

ArrayList and vector both are dynamically growing arrays.
ArrayList is not thread safe where as vector is thread safe.
vector is legacy class and ArrayList is newly added.
by default ArrayList capacity is 0 where as Vector intial 
capacity is 10.
vector is growing by its size doubled.
ArrayList is increse by its size half(50%)

ArrayList is having only those method defined within its
collection class but in case of vector it is having its own
method which is not a part of its collection class.

import java.util.*;
public class VectorDemo{
  public static void main(String[] args){
    Vector<Object> vector = new Vector<Object>();
    int primitiveType = 10;
    Integer wrapperType = new Integer(20);
    String str = "tapan joshi";
    vector.add(primitiveType);
    vector.add(wrapperType);
    vector.add(str);
    vector.add(2, new Integer(30));
    System.out.println("the elements of vector: " + vector);
    System.out.println("The size of vector are: " + 
vector.size());
    System.out.println("The elements at position 2 is: " + 
vector.elementAt(2));
    System.out.println("The first element of vector is: " + 
vector.firstElement());
    System.out.println("The last element of vector is: " + 
vector.lastElement());
    vector.removeElementAt(2);
    Enumeration e=vector.elements();
    System.out.println("The elements of vector: " + vector);
    while(e.hasMoreElements()){
      System.out.println("The elements are: " + 
e.nextElement());
    }  
  }
}

Arraylist also has the initial capacity as 10.
Please check the following code in ArrayList class:

public ArrayList() {
	this(10);
    }