I almost agree with psvt, but reading the first book, I had the feeling that Varys let the first Hand die (and hated to do so, but let the second one be imprisoned, concocted the whole "go-to-The-Wall" scheme and ended up facepalmed by Joffrey's egotrip execution) so as to not weaken the throne, but to prevent Cersei's children being revealed as bastards, since the next person rightfully in sucession (Stannis) would put the kingdoms at war and destroy his carefully plans.
Varys states clearly to Ned that he would save him, if it wasn't for the fact that Ned Stark honor demands that Joffrey is pointed as a bastard, bringing Stannis to court, and that Stannis would immediately wage war against half of Westeros, including but surpassing Lannisters, the last Targaryens across the sea, the dozens of lords and lord heirs now peaceful and forgiven that sided Aerys decades ago and that Stannis, kind of bitchy, always tried to convince Robert to burn Cersei alive or something as sweet...
Long talk short, Varys says that he had his share of "righteous war" when he had to witness the Targaryen childrens killed, specially the little girl's raping and awfull death, and that he would prefer to see a stupid bastard as king instead of a rightful but, ultimately, war-driven king. The "just king" would also probably lead to his execution (himself a very probable victim for Stannis' hatred, as a spy and a former Targaryen councilman).
It's quite the moment for me, since Varys, 'til that moment a bidimensional, scheming for sport guy, finally acknowledges that Stark is such a righteous, honest, trustworthy man, who will never live enough to use these facts to manipulate the Spider, that he can take a break on pretending and tell him something from the heart about his mental state, process and traumas (he does it less freely to Tyrion, and with some disguising smiles).
In his words, he wants Westeros at peace, and Joffrey is an adequate lazy king to warm the throne while other plans are unfolding across the sea. I'm not sure if he can imagine Daenerys' outcome or if he was hoping for Viserys, but he clearly is rooting for Targaryens, since Ned gets infuriated and says he can't trust someone who is always changing loyalties, only to be met with Varys' smile and a kind of cryptic "I'm still loyal to the same house" answer.
Sorry for my lame English, I'm still learning. Hope it didn't sound cocky or stupid because of my language.