A regular debate among digital artists is Photoshop vs. Painter - what's the best choice? The main argument for Painter is that it does a great job at emulating real-world materials. There's no doubt that Painter can accurately recreate watercolors, oil pastels, and other media.
But I hate Painter. It's painfully slow and awkward to use. So here's a tutorial on how to make three-dimensional paintstrokes using Photoshop.
Start a new file. Right away, create a new layer, and make sure it's set to transparent, not white-filled. Choose an appropriate brush. If you have Photoshop 7 or CS, you get a nice variety of natural brushes to choose from, like this one:

If you have an earlier Photoshop, you can still download good brushes, or make do with the normal ones.
Paint a stroke:

Go into the Layer Effects menu. Choose Bevel & Emboss. Depending on what resolution you are working in, you can adjust the size slider to change how thick the paint should look. I changed the Highlight Mode from Screen to Overlay in this example, it looks less 'plasticy'.
After that, move over to Drop Shadow, and apply that too. Set the distance slider very low so the paint doesn't look like it's floating.

And that's it, you've got a 3D paint stroke.
Of course, you can get creative and fancy with the concept. Back in Bevel & Emboss, there's a sub-category called Texture. There, you add a bump effect to the paint. Choose an appropriate texture, and slide the depth down to around 5-10% will usually give you the best look:

I also added a Gradient Overlay at a low percentage, and the result is the decent looking turd you see above.
So when working on your paintings, create a new layer for each separate area, and vary the opacity, depth, and texture for each layer. The layers will begin to blend into one another and, with practice, you will get the real-media effect you are looking for.

As a finished example, here's an abstract wallpaper made with this technique:

(click for full-size version)
And here's a devilish concept painting, where you'll note the 3D paintstrokes in the flames.

And with this example in mind, you can now literally tell Painter to go to hell.