I would like to take pictures on my 35mm film camera that are wider/longer. Is there any way to do that on a film camera without just cropping the photo? Can I use different sizes on film on my camera or would i have to buy a whole new camera?
The size of the photo depend of frame, which is inside the camera, usually between shutter and film. So to make panorama like photo (if this is what you mean by "wider/longer") you should crop the photo. Here is example of this "frame"
Or buy new camera which is created for such kind of photos.
EDIT: You can use one "hack" putting two bands of nontransparent material on the upper and lower part of this frame. But this will move the film slightly behind (loose focus), put in dangerous to scratch the film. And at the end there will be no different than crop in postproduction :)
Edit 2: "Using" answer from Horitsu you can buy anamorphic lens. Unfortunately those lens are quite expensive (> 500 USD/Euro) and often they come as adapter to particular lens. The downside is you should use anamorphic lens with same ratio when you print your photos on paper or stretch the scan in postproduction.
A roll of film is fully "photosensitive". It's not the case that there are predefined "frames" where a photo can appear - the size of the frame that is exposed depends explicitly on the camera - you can't buy "panoramic film". There are cameras that expose different frame sizes, but the standard size for cameras using 135 film is 24mm x 36mm.
If you are looking for a camera that exposes a wider image, take a look at the Hasselblad XPan (aka Fuji TX-1) or Hasselblad XPan II (aka Fuji TX-2). This is a discontinued camera, and a used (working) one will not be cheap. It exposes wider frames by essentially using medium format lenses (or rather, lenses that project an image circle wide enough for medium format). The Lomographic Society offers some cameras that will expose the image over the film's sprocket holes. Look for their "Sprocket Rocket" camera series - this can be a less expensive way of experimenting in this area.
There are also rotating-lens panoramic cameras, where the lens is in a kind of turret that rotates when you take a photo. A much wider strip of film is exposed. The Lomographic Society also offers one or two models in this category, called "Horizon". I own a Noblex 135 S and I love the results I get with it. This is a quirky style of photography, with its own idiosyncrasies - and possibly not to everyone's taste.
Note that developing film is the same regardless of what camera is used, but printing/scanning images may not be as straightforward when the frames are not standard 24mm x 36mm.
It would probably be worth your while reading this related (duplicate?) question, and my answer there:
Wide aspect ratio (not panorama) 135 camera?
There are purpose-made cameras that shoot very wide format shots on 35mm film, e.g. the Hasselblad XPAN, which shoots a 24x65mm image (standard 35mm format is 24x36mm).
Another option is a medium format camera with a wide-format 35mm back, such as the Bronica SQ series with the 135W back. It shoots about 24x58mm (I'm estimating the second measurement, but it'll be just shy of 60mm since the system is designed for 6x6cm rollfilm). These backs seem rare and quite expensive, which is unfortunate, since I'd love to have one for my SQ system. :)
Of course, you can just shoot standard 35mm images and crop the top and bottom (some cameras will have a built-in mask system that will do this for you, but you can simply do this yourself). You can also shoot larger formats, like 120 rollfilm, and do the cropping yourself and maintain higher quality, since you're using a larger negative.