A person who doesn't want to get married (duh!)
Marriage is a choice and as with many choices that we make in life, there is a yes option and a no option. Know that some people just don't want to get married. You shouldn't have to beg, bribe, lure, blackmail, or badger someone into marrying you, nor should you assume that just because you've dated so many years, that means this is clearly the time it should happen. Listen very carefully to someone who lets you know, they want nothing to do with marriage. There's nothing wrong with you wanting to get married, and you should never be made to feel ashamed for wanting a life where you are married, but you just may need to definitely look elsewhere if it is something that is that important to you.
A person who's "in love" with their mom (or family)
Just about every person can appreciate a partner who loves their mom or their family. It's often a very good sign that this is a person who is going to show you the same love and respect that he or she shows for their own mother/family, but there is the person who loves their mom and the person "in love" with her. The latter puts absolutely no boundaries on their relationship. Mom can come over any time she wants, she has rights to make rules and control your house when she's over, your partner always sides with their mom no matter if she's totally in the wrong or absolutely crossing the line, they call each other six or seven times a day, they still go over to her house to do laundry or eat (and don't bother to even invite you), s/he uses their mom as their personal shrink often talking about your own personal private problems and then mortified, you hear about them from her and what she thinks you need to do to fix them.
It is clear in no uncertain terms that for the rest of your life, you will always be number two to their mom or family no matter what, even though you're married to each other and not the family. Pass on this one unless you want to spend your entire life trying to fight for a spot at the table.
A partner dealing with addiction or chronic depression
Sometimes there is a time, place, and a season to be with certain people. When your partner is in the middle of a crippling depression or dealing with an intense addiction, this may not be the prime time to decide to get into a long term marriage. When someone is dealing with addiction, their drug of choice is much stronger than anything and anyone around them. Food, sex, drugs, alcohol, technology, etc. These are people who can't stop and can't walk away. They want, nay, need that thing, more than they so a healthy connected relationship and if you come along, you may find yourself not getting anything in return.
Even someone entering into recovery has a lot going on and needs to focus on their sobriety. It's needs to not be about you in that time in their life. Often times they will try to replace their addictions with becoming addicted to something else, like you. Sounds great, but it becomes like an obsession and when you disappoint or don't come through or aren't there as their everything, every second, all the time, you can get royally burned.
With chronic depression, your partner may be dealing with issues well above your pay grade, and there is no shame in admitting that you don't have the tools to help them deal with what they are dealing with. You can still support them, but hold off on or don't marry them. They may be dealing with things that even they don't know how to understand as going on with them or they may not be able to make sense of their lives or how you can fit into that life anymore.
You may faced with the impossible task of trying to hold them up all the time as well as deal with whatever is going on with your own life, kids, work, the rest of the world. You just may end up basically dating yourself because the other person is so checked out of their own lives to even recognize you as existing anymore which can be extremely painful.
A partner who's job is their spouse
Even with the most demanding jobs on earth, if a person wants to be in a relationship with another human being, they must want to give up some of their time to the other person freely and without reserve or feeling like its a hardship. Don't misunderstand, a lot of couples go through periods, where one or the other or both, have to go at it hard in order to build up to something bigger, or to get those dream jobs, or provide for the family, but even then, you should be able to say to one another, every Wednesday, for example, is our time to connect, if that's all we have, and you stick to it.
All work and no play makes a sour relationship because the other person will start to feel like, if they haven't already, that they have no priority in your life if they aren't something to do with work. Meaning, your calls and texts go unanswered, but if you were to call right back from the office phone, they pick up right away.
Anyone with a case of the me, me, mes
It takes two to tango in a marriage. Your partner gives, you give. You figure out a healthy split of responsibilities. You support them, they support you in what you do. If there is not a good balance and one partner is just expecting that you need to always be there for them and do what they want, but when the tables are turned, they are a constant no show, don't seem to have much respect for what's important to you, or feel like your needs are a burden, do NOT marry this person. They are, or at least, have really narcissistic tendencies, and can't be bothered to see a world that revolves around anyone but themselves.
If you are in a relationship right now with someone you know or find out has been double timing you by still dating someone else or is worse, still married to someone else, get those big dumb stars out of your eyes. If they are willing to do what they are doing to someone else with you now, really honestly, don't be surprised when they get bored or need to get their rocks off with something new, and do the same thing to you. Yes, once a cheater, always a cheater. People can change over time, but that time certainly doesn't happen in between their spouses sheets and your own.