It is not clear which command you removed. If you removed
\draw (0,0) .. controls (1,1) and (2,1) .. (2,0);
that should be fine. I can't test any of this because you didn't provide a complete minimal example, but it should work fine.
If you tried
\draw (0,0) .. .. (2,0);
\draw (0,0) .. (2,0);
then it will not work. It would be helpful if you said how it failed. Which error message did you get, for example?
The problem here is that you are requesting a curve but providing no information about its shape. So TikZ cannot construct it.
\draw (0,0) -- (2,0);
should work because the end points is all the information needed to construct a straight line.
If you just wrote
(0,0) circle [radius=2pt]
(1,1) circle [radius=2pt]
(2,1) circle [radius=2pt]
(2,0) circle [radius=2pt];
as the sole content of a
tikzpicture, then the problem is that you haven't issued any command at all and TikZ does not know how to parse the coordinates etc. outside of any command context.
That is, TikZ/PGF parses the instructions it receives in a way that is context-sensitive. It depends on, among other things, the kind of thing it is constructing.
The above code specifies some coordinates, but without telling TikZ to expect a coordinate. So TikZ doesn't know they are meant to be coordinates. It also specifies the size and shape of some parts of a path, but without telling TikZ that it should construct a path. So TikZ doesn't know that these are meant to be part of a path specification.
In isolation, the code is meaningless. It only makes sense if you first tell TikZ it is going to be making a path using, for example,
I asked How does one pick control points to control Bézier curves in TikZ? and the answer there may be of assistance.
However, if you are trying to learn TikZ without ever opening the manual i.e. purely from examples, then you may find it a painful experience. If you don't understand how something works, look it up in the manual. The documentation is generally very good. Overwhelming, yes, but fantastic as a reference.