Healthcare or Health care ? Which one is correct?
Both are correct, as well as health-care. There is no difference in meaning between them.
This article sheds some light. It seems that the expression is in the slow process of being converted from the combination of two words into a word in itself.
Three years after this post, the "health care" vs. "healthcare" question is still very relevant.
The article linked by @Guffa is a helpful reference. The original link is broken, but it can still be found here.
The article points out that -- as of 2011 -- The Associated Press (AP) prefers the open form, "health care", while Reuters prefers the closed form, "healthcare".
I just checked myself, and sure enough the AP still almost exclusively uses "health care". Conversely, a search on the Reuters website shows their articles using "healthcare" 80% of the time over "health care".
Although "health care" is still commonly used, it is argued that the closed form, "healthcare", is on its way to becoming the standard in the same way we've seen words such as "web site" become "website" (the latter gained official approval by the AP in 2010).