Vectors and matrices can only be of a single type and cbind and rbind on vectors will give matrices. In these cases, the numeric values will be promoted to character values since that type will hold all the values.
(Note that in your rbind example, the promotion happens within the c call:
> c(10, "[]", "[[1,2]]")
[1] "10" "[]" "[[1,2]]"
If you want a rectangular structure where the columns can be different types, you want a data.frame. Any of the following should get you what you want:
> x = data.frame(v1=c(10, 20), v2=c("[]", "[]"), v3=c("[[1,2]]","[[1,3]]"))
> x
v1 v2 v3
1 10 [] [[1,2]]
2 20 [] [[1,3]]
> str(x)
'data.frame': 2 obs. of 3 variables:
$ v1: num 10 20
$ v2: Factor w/ 1 level "[]": 1 1
$ v3: Factor w/ 2 levels "[[1,2]]","[[1,3]]": 1 2
or (using specifically the data.frame version of cbind)
> x = cbind.data.frame(c(10, 20), c("[]", "[]"), c("[[1,2]]","[[1,3]]"))
> x
c(10, 20) c("[]", "[]") c("[[1,2]]", "[[1,3]]")
1 10 [] [[1,2]]
2 20 [] [[1,3]]
> str(x)
'data.frame': 2 obs. of 3 variables:
$ c(10, 20) : num 10 20
$ c("[]", "[]") : Factor w/ 1 level "[]": 1 1
$ c("[[1,2]]", "[[1,3]]"): Factor w/ 2 levels "[[1,2]]","[[1,3]]": 1 2
or (using cbind, but making the first a data.frame so that it combines as data.frames do):
> x = cbind(data.frame(c(10, 20)), c("[]", "[]"), c("[[1,2]]","[[1,3]]"))
> x
c.10..20. c("[]", "[]") c("[[1,2]]", "[[1,3]]")
1 10 [] [[1,2]]
2 20 [] [[1,3]]
> str(x)
'data.frame': 2 obs. of 3 variables:
$ c.10..20. : num 10 20
$ c("[]", "[]") : Factor w/ 1 level "[]": 1 1
$ c("[[1,2]]", "[[1,3]]"): Factor w/ 2 levels "[[1,2]]","[[1,3]]": 1 2