You could probably use almost any type of paper but you won't necessarily get the best results.
Inkjet printers deliver exactly the right amount of ink to match the surface of the paper that you've told it you're using (such as high gloss paper or matt photo paper, for example). Each requires a different quantity of ink, distributed in different droplet sizes. You'll get far better results by using proper inkjet printing paper than you will by using ordinary 'copy' paper but you'll get even better results by using a really good quality photo paper.
Using laser paper will probably result in a similar quality output to using ordinary copy paper (e.g. good enough for producing throwaway black-&-white 'hand outs' for a meeting but nowhere near good enough for sending your letter of application for an important job or for producing decent colour graphics).