These come in a few forms, for example, once the mission Tuchanka: Bomb becomes available, you have until you've completed 3 more missions to finish it. After that point, you can no longer complete that mission, with all of the attendant consequences. Most other side missions will 'expire' eventually if you progress the critical path too far while neglecting them. Such expiration is the rule, not the exception.
In addition, many of the minor fetch-quests scattered about the Citadel can only be completed before certain major storyline events. In general, it's best to complete these as soon as they become available, as the NPC's involved in them can and will disappear without notice after a variety of triggers along the critical path.
From what I've seen, there are no explicitly 'urgent' missions like this along the main quest path, so, for the most part, if you do all side quests as they become available, you'll be fine. In a few cases, such as after Priority: Sur'Kesh, the critical path branches, and you must complete one of two missions before continuing. In this case, you'll generally have the option of completing both, so long as you do not continue on to the mission unlocked by completing the first of the two.
The notable 'exception' to all of this is that you should always check in on people in the Citadel, such as your wounded squadmate, as soon as possible. The window of time in which you can do so is often narrow, and your conversations with them (or lack thereof) will have serious implications as you continue with the games primary narrative.
There is one other notable consideration: If you delay certain storyline or DLC missions for too long, you may find that you don't have enough conversation opportunities with squadmates recruited after those events to unlock all of their bonus powers. This is especially easy to have happen with Tali and Javik. It may be worth doing Eden Prime and Rannoch as soon as they are available and you have completed any side missions which the completion of those will lock you out of.