merge/combine columns with same name but incomplete data

Nobody's posted a dplyr solution, so here's a succinct option in dplyr. The approach is simply to do a full_join that combines all rows, then group and summarise to remove the redundant missing cells.

library(tidyverse)
df1 <- structure(list(ID = 1:5, hello = c(NA, NA, 10L, 4L, NA), world = c(NA, NA, 8L, 17L, NA), hockey = c(7L, 2L, 8L, 5L, 3L), soccer = c(4L, 5L, 23L, 12L, 43L)), row.names = c(NA, -5L), class = c("tbl_df", "tbl", "data.frame"), spec = structure(list(cols = list(ID = structure(list(), class = c("collector_integer", "collector")), hello = structure(list(), class = c("collector_integer", "collector")), world = structure(list(), class = c("collector_integer", "collector")), hockey = structure(list(), class = c("collector_integer", "collector")), soccer = structure(list(), class = c("collector_integer", "collector"))), default = structure(list(), class = c("collector_guess", "collector"))), class = "col_spec"))
df2 <- structure(list(ID = 1:5, hello = c(2L, 5L, NA, NA, 9L), world = c(3L, 1L, NA, NA, 7L), football = c(43L, 24L, 2L, 5L, 12L), baseball = c(6L, 32L, 23L, 15L, 2L)), row.names = c(NA, -5L), class = c("tbl_df", "tbl", "data.frame"), spec = structure(list(cols = list(ID = structure(list(), class = c("collector_integer", "collector")), hello = structure(list(), class = c("collector_integer", "collector")), world = structure(list(), class = c("collector_integer", "collector")), football = structure(list(), class = c("collector_integer", "collector")), baseball = structure(list(), class = c("collector_integer", "collector"))), default = structure(list(), class = c("collector_guess", "collector"))), class = "col_spec"))

df1 %>%
  full_join(df2, by = intersect(colnames(df1), colnames(df2))) %>%
  group_by(ID) %>%
  summarize_all(na.omit)
#> # A tibble: 5 x 7
#>      ID hello world hockey soccer football baseball
#>   <int> <int> <int>  <int>  <int>    <int>    <int>
#> 1     1     2     3      7      4       43        6
#> 2     2     5     1      2      5       24       32
#> 3     3    10     8      8     23        2       23
#> 4     4     4    17      5     12        5       15
#> 5     5     9     7      3     43       12        2

Created on 2018-07-13 by the reprex package (v0.2.0).

Here's an approach that involves melting your data, merging the molten data, and using dcast to get it back to a wide form. I've added comments to help understand what is going on.

## Required packages
library(data.table)
library(reshape2)

dcast.data.table(
  merge(
    ## melt the first data.frame and set the key as ID and variable
    setkey(melt(as.data.table(df1), id.vars = "ID"), ID, variable), 
    ## melt the second data.frame
    melt(as.data.table(df2), id.vars = "ID"), 
    ## you'll have 2 value columns...
    all = TRUE)[, value := ifelse(
      ## ... combine them into 1 with ifelse
      is.na(value.x), value.y, value.x)], 
  ## This is your reshaping formula
  ID ~ variable, value.var = "value")
#    ID hello world football baseball hockey soccer
# 1:  1     2     3       43        6      7      4
# 2:  2     5     1       24       32      2      5
# 3:  3    10     8        2       23      8     23
# 4:  4     4    17        5       15      5     12
# 5:  5     9     7       12       23      3     43