Usually vectors are only created in vector-based programs such as Adobe Illustrator or Inkscape, with some limited support for drawing vectors in programs like Adobe Fireworks and Flash.
However, can Photoshop be used for vector purposes? Would it be optimal to do all your vector-based image creation there, for example, considering that it might be later on used in the project in a web design layout?
Photoshop has support for vectors, or as it calls them 'paths'
There is a pen tool for drawing paths freeform, text tool, shape tools and selection tools for editing previously laid paths.
Once you have a path laid you can fill it with a colour or apply layer effects to it non destructively.
So the basics are there, but Illustrator and other programs have much more advanced tools for editing those vectors. Also photoshop only outputs as its own psd format or a flat image. The only way you can export paths to another program is as an illustrator file.
So for simple things or if that's the only program you have access to, go for it! You might find yourself in Illustrator never using any of the features that PS doesn't have. But once you really get into the things you can do with Illustrator it's hard to go back!
Old question, I know.. but it's worth pointing out....
Photoshop does have vector tools and can save some vector content in some formats (psd, pdf, eps). However, Photoshop will never create a true vector file.
What Photoshop creates are vector containers with raster content. This is dramatically different than a vector container with a vector content. For example, Adobe Illustrator will create a vector shape with a vector gradient within that shape. That means when the shape is resized upon output, the gradient is recalculated to match the new boundaries. What Photoshop does is, upon output, recalculates the vector container yet merely scaled the raster contents in the container. This can result in "broken pixels" for the interior appearance.
While you certainly can use vector tools within Photoshop to make rescaling and sizing inside Photoshop easier and more resolution independent. The important difference is output and scaling upon output. A Photoshop EPS or PDF file is nowhere near the same thing as an Illustrator EPS or PDF file. The internal construction of elements is dramatically different. Photoshop is okay in a pinch, but it's not the best tool if you have others available.
Fireworks and Flash both also contain vector tools. However, neither Fireworks nor Flash are designed for print output. If you are creating a project for print. I would never use either of these apps for anything since the content is not created in a manner which allows print output.
If you need true vector files, you are always better off using a true vector application such as Illustrator, Freehand, Inkscape, CorelDraw, Xara, etc.
Photoshop has vector tools that are particularly useful for advanced masking and channel methods. You can also export paths to illustrator and work on them there, where illustrator has a much more robust vector toolset.
One way I've found vectors in photoshop work very well is to create a vector mask then record a function that will apply open all of the images in a folder, apply the mask, resize the to a standardized size, then save in another directory to batch image thumbnails extremely quickly. This is really good for making product thumbnails, user icons, etc for websites. You can also add in some minor image optimizations into the function like auto-level adjustment, etc. Which are beyond the scope of doing the same task in Illustrator.
Additionally:
You can import your .psd with layers in Illustrator in the new version of Illustrator.
It should make the text in vector if you select "convert layers to objects."
This is really only a "lifesaver." Photoshop is made to be used for images not vectors, but it has some basic vector tools as clearly mentioned in all the other answers and comments.
Yes it can, but Adobe Illustrator or Adobe Fireworks have better vector tools.
The problem i had with Photoshop and Illustrator (and lately with fireworks) for the web is that they always mess with the points and sizes. I can't produce a 1-pixel exact image.
Whenever I make a header shape of 100,10 in 50,5 I end with a shape with 101x11 or 99x10; I think is because Photoshop and Illustrator are meant for printed material so 1 pixel is not big enough for them to make a difference but for the web and CG 1 pixel is big enough to make things looks awkward (like gaps between shapes).
