Basically, your body can extract and use the water from anything that has water in it (including solid foods) to meet your water needs. So, the question is not really whether something other than plain water "counts" as water, but rather, whether the other stuff that comes with it makes it a good choice for your needs and goals.
Some beverages, such as those with high caffeine or alcohol content (both diuretics), may also increase the amount of water your body eliminates without using, so that needs to be taken into account. Some beverages provide "empty" calories (added sugar) that need to be counted, and some provided needed nutrients. Others such as Crystal Lite and Kool-Aid use artificial sweeteners to provide flavor without calories, which appears to be safe in moderation, but could potentially cause problems if used excessively.
Here's an article from our SP Dietitian, Becky, with more info: Healthy Beverage Guidelines
Hope this helps!