Advertising
Most free web hosts impose advertising on your website. This is done to cover the costs of providing your site the free web space and associated services. Some hosts require you to place a banner on your pages, others display a window that pops up everytime a page on your site loads, while still others impose an advertising frame on your site. There is really no hard and fast rule which is to be preferred: some people hate a pop-up window, other webmasters dislike having to stuff banner codes onto their pages, and many people cannot stand an advertising frame (which may cause problems when you submit your website to search engines). Whichever method is used, check that you're comfortable with the method.
Note that free web hosts without forced advertisements aren't necessarily good news. Without a viable means to recover the costs of running their server, many of them close with alarming frequency.
Amount of web space
Does it have enough space for your needs? If you envisage that you will expand your site eventually, you might want to cater for future expansion. Most sites use less than 5MB of web space. Indeed, at one time, one of my other web sites, thefreecountry.com, used less than 5MB of space although it had about 150 pages on the site. Your needs will vary, depending on how many pictures your pages use, whether you need sound files, video clips, etc.