All the numbers that fit in a string

Pyth, 57 bytes

j-f:T"^0$|^-?([1-9]\d*)?(\.\d*[1-9])?$"0{.P*Q+jkUT".-"Q\-

Try it on the online interpreter.

Way too long, and with horrific runtime (takes several seconds for N=4, running with N=5 is not recommended).

            .P           Q    all permutations of length (input) of
                 jkUT         ... the string "0123456789"
                +    ".-"     ... plus the chars "." and "-"
              *Q              ... whole thing times the input -- pyth has
                              no repeated_permutation, so this is necessary
           {                  uniquify
  f                           filter by
   :T"..."0                   does it match the really long regex?
 -                        \-  get rid of "-"
j                             join on newline

Regex explanation:

^0$|            "0", or...
^
 -?             optional negative sign
 ([1-9]\d*)?    optional part-before-decimal
 (\.\d*[1-9])?  optional part-after-decimal
$

Julia, 126 117 bytes

n->filter(i->ismatch(r"^0$|^-?([1-9]\d*)?(\.\d*[1-9])?$",i)&&i!="-",∪(map(join,combinations((".-"join(0:9))^n,n))))

This is a lambda function that accepts an integer and returns an array of strings. To call it, assign it to a variable. The approach here is the same as Doorknob's Pyth answer.

Ungolfed:

function g(n::Int)
    # Get all n-character combinations of .-0123456789
    c = combinations((".-"join(0:9))^n, n)

    # Join each group of n characters into a string and take unique
    u = ∪(map(join, c))

    # Filter to only appropriately formatted strings
    filter(i -> ismatch(r"^0$|^-?([1-9]\d*)?(\.\d*[1-9])?$", i) && i != "-", u)
end

Pyth, 47 45 bytes

Thanks to FryAmTheEggman for noting that the order does not matter.

jf!sm:Td)c".- \..*\. ^-?0. [.-]0*$"d^{`c_T17Q

Try it online.

The runtime is horrible, basically O(12ⁿ), but I tested it for n = 6 on my computer (which took 2 minutes). Running n ≥ 5 will time out online.

Due to the way I generate the characters 0123456789.- the output is in a really weird order.

One could technically remove the { near the end, but it would result in a complexity of O(19ⁿ). (It would also produce lots of duplicates, but that's allowed.)

Explanation

                  _T       -10
                 c  17     -10 / 17 = -0.5882352941176471
                `          representation: "-0.5882352941176471"
               {           uniquify: "-0.582394176"
              ^       Q    input'th Cartesian power
 f                         filter on:
         c"…"d               split this string by spaces
    m:Td)                    check if the parts match the current string
  !s                         true if none of the parts matched
j                            join by newlines

The main part of the code is ".- \..*\. ^-?0. [.-]0*$", which contains the regexes any output must not match.

.-         minus must be first character
\..*\.     there may only be one decimal point
^-?0.      no extra leading zeroes
[.-]0*$    number must not end with decimal/minus and 0+ zeroes