Before yesterday everything worked just fine, but now I can't create curves. I have drawn several lines with the beizer tool and tried to edit them to be curves, but the lines remain straight. Trying to edit the handles does nothing, the lines remains straight. The handles can be at any angle but they have no effect on the line. Even if I try making a curve by clicking and dragging to make a handle, and then clicking elsewhere to make the curve, it draws only a straight line. The only way for me to make a curve is when I Ctrl-click on a node between two other nodes, and even then I have no way to use the handles.

Oddly enough, when I edit something that I drew before yesterday, I can make curves as easily as before. However, anything that I've drawn since then can't curve at all.

Check to see if your control for the bezier tool's "Mode" is not set to either the straight line or the rightangled line setting. Although you should still be able to click with the node tool between two nodes and drag the line into a curve!
Your problem is probably more serious than this simple fix...

Deactivate 'Spiro mode' for new curves or convert the cusp nodes into smooth ones if you want to use the 'Spiro' effect.

a friendly note,

It is essential to pay attention to the Tool Controls Bar when using Inkscape (or any other editor). The issue you are likely having is that your Bezier tool is in "Spiro" Mode as ~suv pointed out.

When I first started using inkscape there were two areas of the interface I ignored and now they are essential to my fun in Inkscape.

The two areas are the Tool Controls Bar (above the canvas) and the Notification Display. The Notification Display (below the canvas area - bottom center) is awesome and will coach you through using inkscape dynamically. Just using a single edit this area could display up to 4 different notifications to help you use Inkscape's POWER!!! If you are on a laptop and you can't read the full text simply float your mouse over the message and a pop-up will display all the text of the notification..

Hope this helps...

Thanks for the help everyone, thats was a little bit embarrassing. I'm still getting used to Inkscape's new controls, and I guess I accidentally clicked on the spiro tool (which I wasn't even aware existed until today). Good to know that I won't have to re-install Inkscape or anything of that sort, I'll know what to do next time as well.