To summarize the other answers and combine them with what I know, I found 10 main ways to do this (see below). Also, I wrote some performance tests (see results below). For example, if we want to find the sum of all of the keys and values of a map, we can write:

1. Using iterator and Map.Entry

   long i = 0;
   Iterator<Map.Entry<Integer, Integer>> it = map.entrySet().iterator();
   while (it.hasNext()) {
       Map.Entry<Integer, Integer> pair = it.next();
       i += pair.getKey() + pair.getValue();
   }
   

2. Using foreach and Map.Entry

   long i = 0;
   for (Map.Entry<Integer, Integer> pair : map.entrySet()) {
       i += pair.getKey() + pair.getValue();
   }
   

3. Using forEach from Java 8

   final long[] i = {0};
   map.forEach((k, v) -> i[0] += k + v);
   

4. Using keySet and foreach

   long i = 0;
   for (Integer key : map.keySet()) {
       i += key + map.get(key);
   }
   

5. Using keySet and iterator

   long i = 0;
   Iterator<Integer> itr2 = map.keySet().iterator();
   while (itr2.hasNext()) {
       Integer key = itr2.next();
       i += key + map.get(key);
   }
   

6. Using for and Map.Entry

   long i = 0;
   for (Iterator<Map.Entry<Integer, Integer>> entries = map.entrySet().iterator(); entries.hasNext(); ) {
       Map.Entry<Integer, Integer> entry = entries.next();
       i += entry.getKey() + entry.getValue();
   }
   

7. Using the Java 8 Stream API

   final long[] i = {0};
   map.entrySet().stream().forEach(e -> i[0] += e.getKey() + e.getValue());
   

8. Using the Java 8 Stream API parallel

   final long[] i = {0};
   map.entrySet().stream().parallel().forEach(e -> i[0] += e.getKey() + e.getValue());
   

9. Using IterableMap of Apache Collections

   long i = 0;
   MapIterator<Integer, Integer> it = iterableMap.mapIterator();
   while (it.hasNext()) {
       i += it.next() + it.getValue();
   }
   

10. Using MutableMap of Eclipse (CS) collections

    final long[] i = {0};
    mutableMap.forEachKeyValue((key, value) -> {
        i[0] += key + value;
    });
    

Perfomance tests (mode = AverageTime, system = Windows 8.1 64-bit, Intel i7-4790 3.60 GHz, 16 GB)

1. For a small map (100 elements), score 0.308 is the best

   Benchmark                          Mode  Cnt  Score    Error  Units
   test3_UsingForEachAndJava8         avgt  10   0.308 ±  0.021  µs/op
   test10_UsingEclipseMap             avgt  10   0.309 ±  0.009  µs/op
   test1_UsingWhileAndMapEntry        avgt  10   0.380 ±  0.014  µs/op
   test6_UsingForAndIterator          avgt  10   0.387 ±  0.016  µs/op
   test2_UsingForEachAndMapEntry      avgt  10   0.391 ±  0.023  µs/op
   test7_UsingJava8StreamApi          avgt  10   0.510 ±  0.014  µs/op
   test9_UsingApacheIterableMap       avgt  10   0.524 ±  0.008  µs/op
   test4_UsingKeySetAndForEach        avgt  10   0.816 ±  0.026  µs/op
   test5_UsingKeySetAndIterator       avgt  10   0.863 ±  0.025  µs/op
   test8_UsingJava8StreamApiParallel  avgt  10   5.552 ±  0.185  µs/op
   

2. For a map with 10000 elements, score 37.606 is the best

   Benchmark                           Mode   Cnt  Score      Error   Units
   test10_UsingEclipseMap              avgt   10    37.606 ±   0.790  µs/op
   test3_UsingForEachAndJava8          avgt   10    50.368 ±   0.887  µs/op
   test6_UsingForAndIterator           avgt   10    50.332 ±   0.507  µs/op
   test2_UsingForEachAndMapEntry       avgt   10    51.406 ±   1.032  µs/op
   test1_UsingWhileAndMapEntry         avgt   10    52.538 ±   2.431  µs/op
   test7_UsingJava8StreamApi           avgt   10    54.464 ±   0.712  µs/op
   test4_UsingKeySetAndForEach         avgt   10    79.016 ±  25.345  µs/op
   test5_UsingKeySetAndIterator        avgt   10    91.105 ±  10.220  µs/op
   test8_UsingJava8StreamApiParallel   avgt   10   112.511 ±   0.365  µs/op
   test9_UsingApacheIterableMap        avgt   10   125.714 ±   1.935  µs/op
   

3. For a map with 100000 elements, score 1184.767 is the best

   Benchmark                          Mode   Cnt  Score        Error    Units
   test1_UsingWhileAndMapEntry        avgt   10   1184.767 ±   332.968  µs/op
   test10_UsingEclipseMap             avgt   10   1191.735 ±   304.273  µs/op
   test2_UsingForEachAndMapEntry      avgt   10   1205.815 ±   366.043  µs/op
   test6_UsingForAndIterator          avgt   10   1206.873 ±   367.272  µs/op
   test8_UsingJava8StreamApiParallel  avgt   10   1485.895 ±   233.143  µs/op
   test5_UsingKeySetAndIterator       avgt   10   1540.281 ±   357.497  µs/op
   test4_UsingKeySetAndForEach        avgt   10   1593.342 ±   294.417  µs/op
   test3_UsingForEachAndJava8         avgt   10   1666.296 ±   126.443  µs/op
   test7_UsingJava8StreamApi          avgt   10   1706.676 ±   436.867  µs/op
   test9_UsingApacheIterableMap       avgt   10   3289.866 ±  1445.564  µs/op
   

Graphs (performance tests depending on map size)

Table (perfomance tests depending on map size)

          100     600      1100     1600     2100
test10    0.333    1.631    2.752    5.937    8.024
test3     0.309    1.971    4.147    8.147   10.473
test6     0.372    2.190    4.470    8.322   10.531
test1     0.405    2.237    4.616    8.645   10.707
test2     0.376    2.267    4.809    8.403   10.910
test7     0.473    2.448    5.668    9.790   12.125
test9     0.565    2.830    5.952   13.220   16.965
test4     0.808    5.012    8.813   13.939   17.407
test5     0.810    5.104    8.533   14.064   17.422
test8     5.173   12.499   17.351   24.671   30.403

All tests are on GitHub.