No single specific answer will apply to everyone.
Trying to enumerate the tools that aren't useful in multiples doesn't seem helpful — there are as many valid answers as there are woodworkers. Instead, then, let's consider the criteria that anyone can use to decide whether they need more than one (or zero, two, three, or ten) of a given tool, or conversely, when they don't need more than some number of that tool.
The cost of a tool should be less than the benefit derived from the tool.
The cost of a tool is more than just the purchase price. Every tool takes up some amount of space and many require a certain amount of maintenance.
The primary benefit of a tool is usually that it facilitates some task, but there's also the pleasure of ownership and sometimes the security or convenience of having an extra copy of the tool.
For most tools, the main benefit of owning more than one copy is time.
You can only use one table saw, router, hammer, or 1/8" chisel tip drill bit at a time, so having more than one isn't necessary but might be convenient. Anything that can be done with two routers can be done with one, but having more than one lets you keep one in a router table or use multiple cutters without changing setups. It's hard to swing two hammers at the same time, but having one in the shop, one in your truck, and your tool bucket saves the trouble of moving a single hammer to different sites.
The higher a tool's cost, the harder it is to justify multiples.
It'd be cool to have a second table saw that's always set up for dadoes, but I can't afford to give up that much space in my small shop. This is a case where the convenience of two doesn't match the cost.
It's harder to justify multiples if they can't be used simultaneously.
Clamps are useful in multiples because they're used in parallel. They're more like fixtures than tools in that they do their work after you've operated them. Most tools are useful while they're being operated, which makes it hard for a single woodworker to benefit from more than one at a time. On the other hand, if you ever work with other people, multiples might make a lot of sense.
It's harder to justify multiples of tools that are seldom used.
If a tool isn't used often, you might not even need one, let alone several. A single adjustable finger dovetail jig can be useful enough to justify the cost even if you only use it a few times a year, but a second adjustable finger dovetail jig really doesn't provide any extra utility.