"Here's a draft of X. Please review and provide your feedback by next Tuesday. Thanks."
The recipients will, of course, vary based on exactly what it is, but almost all the time, you really do want input. However, as usual, you're on deadline. So you have to get feedback in what people call "a timely manner". Hence, a deadline. A lot of times you'll get some feedback in time; some of your audience is both sufficiently deadline-oriented and interested in helping achieve the goal of getting a good X together.
Others, well, not so much. Deadlines come and deadlines go, and you hear back quite late or not at all. (By the way, this is rude unless you somehow warn the person requesting feedback and let them know when you really can have it to them.) So what do you do about the people who missed the feedback deadline?
- Ignore them. You can simply not incorporate their feedback and chalk it up to a lost chance to vote. This is generally viable in cases where the person's feedback is likely to be covered by another, or whether the feedback is tangential. If this is your boss, or someone who brings a unique and important view, this may not be something you can do in practice.
- Set a new deadline. Send a follow up mail basically saying, "okay, this time it really is important. Please review by this Friday." Most of the time this doesn't work. The person is no more or less incentivized to do it now. The exception is if your reviewer was simply unavailable (on vacation or something) and is now available; then you might get a response.
- Send a preemptory reminder. A day or so before the initial deadline you set, send out a reminder to those whose feedback you have not yet received. This works best if you send it directly to that person without a cc list; that way you start to overcome any "well, someone else will get to it" mental block. This one actually works rather well; it lends immediacy and personal relevance to the request.
- Whine. This one I really don't recommend, but it is a possible approach. Basically, go to that person's boss (or publicly to the project manager), and try to convince their boss to go make sure they provide feedback. This has a very "whining to mommy" feel to it, and isn't likely to help you get thought-out feedback.
In the end, those are really your choices. Which path you take will depend in large part on the people providing feedback, and the individual(s) from whom you haven't yet seen a response. No magic here, unfortunately, just make your request, follow up on it, and understand that no matter how often or how politely you ask, some people are just not going to bother.