Why is docking permission denied?

I have noticed that under certain conditions a station will deny my docking request.

What are the various conditions that can cause a station to deny a commander's docking request?

If you are more than 7.5 km away from the station when you request docking permission, or if the station has no free landing pads the station will deny your request. Stations will also deny your requests if you've annoyed the controlling faction sufficiently (i.e. you don't have enough reputation with them). As CmdrFreiheit pointed out in the comments, permission can also be denied if your ship is too large to land at the station.

Obviously in the first instance you just need to move closer to the station and try your request again. In the second instance, you could wait for a pad to free up, however if there are a bunch of AFK players there that could take a while. You could instead switch to solo mode and dock, do your stuff, then return to multiplayer. In the third instance you'll have to find some way of raising your reputation with the controlling faction before they will allow you to dock.

In the case of your ship being too large, you'll just have to find somewhere else to dock.

I know this is an ancient question, but it still pops on the first page on Google.

While everything JonK said is absolutely correct, there is a way to "fix" the problem. If too many ships are docked at a station (usually only a problem if you have to land at one of those small stations with only 3 pads), jump in and out of supercruise. This will usually free the pads, unless they are occupied by other players.