Well, as to Dr. Doom, she overwhelmed him with something he wasn't ready for (think a zerg rush in your favorite MMORPG).. When you are armed to shoot down a bomber, 500,000 mosquitoes showing up instead can be an issue...
From the Marvel Wiki entry:
Hundreds of squirrels answered her call and flooded Doom's ship, chewing through the wires, and swamping the evil dictator with their furry bodies. Doom exclaimed "Confound these wretched rodents! For every one I fling away, a dozen more vex me!"
AS to other villains? Yep..
Also from her entry:
Thus far, Squirrel Girl has beaten: Doctor Doom, Mandarin, Giganto, M.O.D.O.K., Thanos, Terrax, Bug-Eyed Voice, Bi-Beast, Deadpool and Pluto.
And... lest you wonder if her victories couldn't be explained away (Doombots, dreams, etc...) the authors like to engage in Lampshade Hanging with them, while clearly documenting their canon status.
Also, see her entry at TvTropes, which contains one my favorite SG moments...
It also creates a Crowning Moment of Funny when she goes to Latveria to borrow Dr. Doom's time machine. Doom just sighs and points her to the room, not even bothering to try and stop her.
Incidentally, if you check out her power stats on the official Marvel.com page for her - they are ALL maxed; this puts her stats on par with various god-like beings such as the Living Tribunal. (Marvel.com, in this case, being about as solidly canon as can be hoped for.)