Summarize other answer and what I know all ways to do this using a one-liner:
   String testString = "a.b.c.d";
1) Using Apache Commons
int apache = StringUtils.countMatches(testString, ".");
System.out.println("apache = " + apache);
2) Using Spring Framework's
int spring = org.springframework.util.StringUtils.countOccurrencesOf(testString, ".");
System.out.println("spring = " + spring);
3) Using replace
int replace = testString.length() - testString.replace(".", "").length();
System.out.println("replace = " + replace);
4) Using replaceAll (case 1)
int replaceAll = testString.replaceAll("[^.]", "").length();
System.out.println("replaceAll = " + replaceAll);
5) Using replaceAll (case 2)
int replaceAllCase2 = testString.length() - testString.replaceAll("\\.", "").length();
System.out.println("replaceAll (second case) = " + replaceAllCase2);
6) Using split
int split = testString.split("\\.",-1).length-1;
System.out.println("split = " + split);
7)  Using Java8 (case 1)
long java8 = testString.chars().filter(ch -> ch =='.').count();
System.out.println("java8 = " + java8);
8)  Using Java8 (case 2), may be better for unicode than case 1
long java8Case2 = testString.codePoints().filter(ch -> ch =='.').count();
System.out.println("java8 (second case) = " + java8Case2);
9)   Using StringTokenizer
int stringTokenizer = new StringTokenizer(" " +testString + " ", ".").countTokens()-1;
System.out.println("stringTokenizer = " + stringTokenizer);
From comment: Be carefull for the StringTokenizer, for a.b.c.d it will work but for a...b.c....d or ...a.b.c.d or a....b......c.....d... or etc. it will not work. It just will count for . between characters just once
More info in github
Perfomance test (using JMH, mode = AverageTime, score 0.010 better then 0.351): 
Benchmark              Mode  Cnt  Score    Error  Units
1. countMatches        avgt    5  0.010 ±  0.001  us/op
2. countOccurrencesOf  avgt    5  0.010 ±  0.001  us/op
3. stringTokenizer     avgt    5  0.028 ±  0.002  us/op
4. java8_1             avgt    5  0.077 ±  0.005  us/op
5. java8_2             avgt    5  0.078 ±  0.003  us/op
6. split               avgt    5  0.137 ±  0.009  us/op
7. replaceAll_2        avgt    5  0.302 ±  0.047  us/op
8. replace             avgt    5  0.303 ±  0.034  us/op
9. replaceAll_1        avgt    5  0.351 ±  0.045  us/op