How can I break a variable definition across multiple lines in a Makefile without spaces?

Not really; the backslash-newline combination is defined to produce a space. However, if you are using GNU Make, you could simply $(subst : ,:,$(CP)).

It’s impossible to prevent backslash-newline from becoming a space, and it’s clumsy and error-prone to try to remove the spaces afterwards (what if there are supposed to be spaces?), but you can remove each as it’s produced. This has the significant advantage of working anywhere, even inside function calls. The trick is to embed the space produced in an expression that expands to nothing.

$(call foo) with empty/undefined foo would work, but we can do better: variable names can contain spaces in (GNU) Make. It’s hard to assign to them, but we don’t want to anyway. So then we can shorten it to $(a b) or even $(a ); a backslash-newline will be turned into a space before the lookup. But even a single space works:

foo=bar$(\
)baz

Finally, the parentheses may be omitted for a single-character variable name:

foo=bar$\
baz

…which finally looks like we are (fully) escaping the newline rather than using it somehow. So long as no one assigns to “ ” (which is even crazier than using it!), anyway.

Sorry to necro this a little bit, but I think this will give you what you're looking for:

CP = .:${HADOOP_HOME}/share/hadoop/common/lib/hadoop-auth-2.2.0.jar:
CP:=$(CP)${HADOOP_HOME}/share/hadoop/hdfs/hadoop-hdfs-2.2.0.jar:
CP:=$(CP)${HADOOP_HOME}/share/hadoop/common/hadoop-common-2.2.0.jar:
CP:=$(CP)${HADOOP_HOME}/share/hadoop/mapreduce/hadoop-mapreduce-client-core-2.2.0.jar:
CP:=$(CP)${HADOOP_HOME}/share/hadoop/mapreduce/lib/hadoop-annotations-2.2.0.jar

This should append the next line onto the value of CP, somewhat different than "+=", which adds a space.