I have been able to play with no problems up until I downloaded Forge so that I could install mods. I successfully logged in and all of the changes were made, showing the "Mods" bar next to the "Texture Packs" bar. However, after placing the Backpacks mod by Eydamos, downloaded from the url http://www.minecraftforum.net/topic/1492661-145-backpacks-v-154/, Minecraft freezes at the screen that says "Updating Minecraft" with the green progress bar at the bottom of the page when I log in. Not only that, the status directly above the bar says "Done Loading." It does this same thing even if I try to play it in-browser on Minecraft.net, not just from my desktop.
Also I have a Minecraft account, not a Mojang account, if that helps at all.