The parallel marker に is used when you're putting together a list of related things (nouns), adding each one as you go. In particular, it gets used if you're trying to think of things (like when you're at a restaurant, trying to think of what food you want to get), and that includes when you're trying to recall at least two things from memory (like if you're trying to remember the names of a couple old friends).
I'm not a native speaker, so I won't try to make up my own examples. I'll take a couple from the 日本語文法ハンドブック:
In this example, the speaker is trying to think of which food they'd like. They list three:
トマト. Note that the last item doesn't have
に. Also pay attention to the
えーと、それから which helps give you the impression that the speaker is trying to think of the items--that's the sort of situation in which you tend to run across
Let's look at another example:
Here again, the speaker is trying to call to mind a list of items. In this case, there are two smaller lists, but they function as one larger list:
フィレンツェ form the first list, and then the speaker thinks of
ヴェネツィア as well, adding them as a second list. In each case,
に is left off the end of the list.
Another example, this time from a video game (Gameboy Wars Advance 2):
The speaker remembers Max and Ewan from the first game, but he hasn't seen them in quite some time. Because he used
に to list the names, you get the sense that he's calling their names to mind from memory. In this case, again the list only has two items, and again
に is omitted from the last item in the list.