Can I buy only the wine glass in the Munich Christmas market?

Even if you pay a deposit for the glass, cup or other tableware, you are supposed to return it and get the deposit back. It does not entitle you to steal the cup, even if you forfeit the deposit by doing so. Deposit for tableware is quite common in Germany, not only at the christmas markets.

There are however usually several places to buy such cups as well, but expect them to cost more than what you pay as deposit.

Edit: Since I didn't expect it to be necessary to justify this answer, I didn't do so or link to any resources, but I seem to be mistaken. I thought it should be obvious what a deposit is and that paying a deposit does not entitle to keep the item. From a legal point of view, there is really no difference between paying a deposit for a wine cup or for a rental car and I also thought it should be obvious that you can not take into possession tableware, which you have provided when going out for something to eat or drink.

When I now google for the subject, it seems to be a common enough misconception, also among Germans, that you can keep tableware for which you have paid a deposit. It is a recurring subject in German law forums and even now and then a topic for newpaper articles. Even if two lawyers usually have three different opinions, they mostly agree on this topic: No, of course you can't keep anything for which you have paid a deposit. If you ask the persons running the booths or markets, their attitude usually lie somewhere between 'we can't prevent that customers take the tableware anyway' and 'if every customer would nick their cup, we would run out of cups three weeks before christmas'. Many christmas markets do not use generic cups, but have special yearly editions made. Even if the deposit is obviously higher than the production costs, you can not automatically infer that it is acceptable to keep the cup. A high deposit can also be used as a mean to get a higher return rate of the tableware. Even if it may appear that a booth operator earns money anyway if the cup is not returned for a high deposit, it may just as well mean that the operator will run out of cups and have no possibility to obtain more cups on a short notice.

Here is a seriously ment legal discussion on the subject (in German) about wether keeping the cup is to be concidered as larceny or embezzlement.

And no, I am not saying that you are likely sent to jail for stealing. Chances are very high that noone will notice or care. However if someone does, they are right and you are wrong. And yes, there is of course no law preventing you from asking the booth if you can keep a cup and they can then decide if it is ok or not.

Theoretically, this is covered by Pfandrecht, in which the merchant takes the role of the creditor (Pfandgläubiger / Sicherungsnehmer) and you take the role of the debitor (Sicherungsgeber). The deposit (Pfand / Sicherheit) is your property but remains in the merchant's possession as long as you possess^[1] the loan (= the cup) under the premise that you will hopefully return the loan at some point.

Now if you do not return the cup, one may have the opinion that this would strictly be (minor) theft since you attempt to (or actually do) take a moveable object that is owned by another person with the intent of taking over ownership illegitimately. That's arguably, within limits, a kinda legitimate point of view. I wouldn't know if that stands in court in presence of Pfand, though.

However, the very intent of the deposit is (BGB §1204) to satisfy the demand of the creditor in case the debitor does not fulfill (i.e. give back the cup). So, very very very strictly, not returning the cup wouldn't count as theft, but would cause Pfandreife. Which means that the merchant will further on be allowed to spend the money you gave them. End of story. That's the reason why every halfway intelligent merchant (or bank) will only ever give a loan that is worth less than the security.

Practically, everybody does it ever now and then, and nobody cares. Taking home your cup is a perfectly "normal" thing, people won't even raise an eyebrow. Contrarily, you can even ask shop runner for a clean cup that you wish to take home and 99.9% certain they'll happily give you one.
In which case BGB §1205 (2) would apply, the deposit being explicitly, and officially transferred and the loan (the cup) being explicitly forfeitet.

Even more practically, even if the merchant -- hypothetically -- humiliated himself insofar as to call police over the cup (for alleged theft) they would not even come, let alone arrest you (even if the theft claim was considered valid). Law enforcement, in reality, is a sad joke in Germany. There's a law against everything, which probably includes breathing in public places.
But in practice, if you have a permanent residence and unless you already have 25 felonies on your record, there's no way you go to prison, let alone for a cup that's worth 30 cents (and for which you paid 3€). Last week, an 48 year old in Siegburg walked free (well, parole, but that's walked free) after being caught distributing child pornography. If you wonder how that could possibly happen, well, he has a permanent residence, first conviction, and he feels honestly sorry.

So, no worries about your little souvenir cup. You're not going to get a life sentence over taking it.

Buying a cup of mulled wine, paying a deposit and then not returning can be considered theft in legal terms.

(German source): https://www.augsburger-allgemeine.de/wirtschaft/Ist-es-Diebstahl-Gluehweintassen-zu-behalten-id36241727.html

At the same time in the article it states and as also stated in the other answers stand owners expect not all of the cups to be returned and they are generally OK with the deposit covering the costs for the cups and it is highly unlikely that you get into trouble for taking a cup instead of returning it.

The solution stated in the quoted article:

Just ASK the stand owner if it is o.k. to take the cup instead of returning it.

They may accept, they may decline or they may ask you to pay 1 or 2 euros on top of the deposit for you to keep it. This way everybody is happy. And don't worry about rusty German. Most stand owners will speak English or you can just ask somebody to ask for you.

Enjoy the Christkindlmarkt!

My experience, also in the North, not just in Munich, is that one can always ask to buy the glass/cup/mug. I have never been refused and am generally given a clean one, often wrapped to prevent breakage. I have even asked on behalf of a non-German speaking friend who wanted one of each type and the stall holders happy to help.

I imagine that the cost of the deposit (Pfand) is less than the replacement cost, so they actually want people to have the mugs.

Or maybe they are just in good mood because it's Christmas time, and they want to be nice to everyone :-)