The whole discussion seems to devolve on whether the empty graph (or empty space) should be considered "connected". Angelo and I are of the school that it should not, but this should be explained since some of the traditional definitions of "connected" apparently allow the empty space to be connected. 

A general abstract context is as follows. Let $C$ be a category with finite coproducts with the property that for any two objects $a$, $b$ (whose coproduct is denoted $a+b$), the canonical functor 

$$C/a \times C/b \to C/(a+b): (x \to a, y \to b) \mapsto (x + y \to a + b)$$ 

is an equivalence. Such a category is said to be *extensive*. The category of topological spaces is extensive, the category of graphs is extensive, any topos is extensive, and there are many, many other examples. 

Now, say an object $a$ in an extensive category to be *connected* if the functor 

$$\hom(a, -): C \to Set$$ 

preserves binary coproducts (whence it can be shown to preserve finite coproducts). This is a fundamental definition; see the <a href="http://ncatlab.org/nlab/show/connected+object">nLab</a> for an extended discussion. Under this definition, the empty space (the empty graph, etc.), i.e., the initial object, is not connected. 

An equivalent definition is to say $c$ is connected if, whenever $c \cong a + b$, exactly one of $a, b$ is inhabited. If one insists that the empty space should be inhabited, then change the word "exactly" to "at most", and instead of saying the canonical map $\hom(c, x) + \hom(c, y) \to \hom(c, x + y)$ is an isomorphism, say it is merely surjective. However, most results come out more cleanly by working with the definition above, which disqualifies the empty set. 

Compare the notion of prime ideal: working in the lattice of ideals of a commutative ring $R$ where $\leq$ is given by reverse inclusion, the coproduct or join of ideals $a, b$ is $ab$, the initial ideal is $R$, and we say an ideal $p$ is *prime* if $p \neq R$ and $p \leq ab$ implies $p \leq a$ or $p \leq b$. The condition $p \neq R$ is considered fundamental to the definition of prime. Without it, we no longer have e.g. unique decomposition of integers into prime factors (compare the fact that every graph is uniquely a coproduct of connected graphs under our definition, but this is not so if the empty graph is considered to be connected). See also the numerous examples in the nLab discussion <a href="http://ncatlab.org/nlab/show/too+simple+to+be+simple">"too simple to be simple"</a>; for example, $1$ is too simple to be a prime, and the zero module is considered too simple to be a simple module.  

Every acyclic graph (a forest) is uniquely a coproduct of acyclic connected graphs (i.e., trees) under our definition of connectedness. This includes the *empty forest*. So a forest can be empty, but a tree cannot.