Beside katanas and longswords I don't know of any others. I define a two handed sword as one designed primarily to be used with two hands. Swords that function as polearms (like zweihanders or flamberges) do not count.

I honestly don't know where to even start. Maybe nodachi and other Japanese sword types larger than katana (which is typically more of a "hand-and-a-half" design usable in one hand just as well as two - just like many European longswords)? European two-handed sabers and messers and estocs? Chinese two-handed jian and dao?

What I'm trying to say is, put short, there's plenty. :)

Listing all the types of primarily two-handed (but smaller than 16th Century Beidenhänder) swords in the world would be quite a bit of work, somewhat redundant and ultimately a futile exercise given all the overlap in form and function and often ambiguous terminology... and, of course, the vast majority of the terms one could mention really just mean "big sword" or "two-hand sword" in the local language (even when the local language is English!) - which reflects the fact that most of them really are ultimately just large swords with a particular local aesthetic.

That said, myArmoury does have a photo album of various European two-handed swords, mostly tucks, claymores and zweihänders, with some spadone and such and also a few bearing swords thrown in...

I do not think all two handers would be used as polearms, the montante techniques are decidedly different. There also is quite a gradual slope between decidedly one handed swords (which can also use a second hand) to swords that are impossible to use onehanded. If a grip is over 10-11cm, you can fit one finger on the grip, and the rest on the pommel and use your second hand that way.

Have you looked at the Oakeshott typology? It describes quite a number of swords that are primarily two handed. On the features page, you can read a good summary. The XIIa, XIIIa, XVa, XVIa, XVII, XVIIIa through e, XX and XXI come to mind. There are messer that are decidedly two handed as well, rivalling longswords in length.

Executioner's sword is about the only example I can think of from Europe that is exclusively 2 handed without filling the role of a polearm. I think you might be having trouble because of the definitions you are using for things. Most swords are meant to be side arms, a "proper" or "real" two handed weapon will, simply because of its size, be unsuitable as a side arm and be the primary weapon of the person carrying it, and most of the time will be used "like a polearm".

A parallel would be asking what modern firearms require the use of two hands, but excluding rifles or weapons that fill the battlefield role of a rifle.