join -1 1 -2 1 -o 1.1,1.2 -t "literalTab" <(sort -k1,1 yourFileWithTwoColumns) <(sort -k1,1 yourFileWithOneColumn) > output

Join on the basis of the first column of file1 (-1 1) and the first column of file2 (-2 1) and output fields 1 and 2 from first file (the rows where first field matched to the first field of the second file). Literal tab is ctrl + v + tab. If your files are already sorted by first field you can skip the sort commands and just give the files as input. Join is orders of magnitude faster than grep when you have two large files as with grep you're going through the second file as many times as there are lines in the first file. If you don't mind creating temp files the above command can maybe be a little bit faster still if you parallelize the sort commands:

sort -k1,1 yourFileWithTwoColumns > yourFileWithTwoColumnsSorted.tmp & \
sort -k1,1 yourFileWithOneColumn > yourFileWithOneColumnSorted.tmp && \
join -1 1 -2 1 -o 1.1,1.2 -t "literalTab" yourFileWithTwoColumnsSorted.tmp yourFileWithOneColumnSorted.tmp > output && \
rm yourFileWithTwoColumnSorted.tmp yourFileWithOneColumnSorted.tmp

The grep command you tried is likely working, but slowly. You could alternatively load both files into R and use inner_join() from the dplyr package. That's relatively quick. Writing a small program to do this in python would also be quite quick. In fact, it'd be something like:

#!/usr/bin/env python
file1="something.txt"
file2="something_else.txt"
IDs = set()

for line in open(file1,"r") :
    IDs.add(line.strip())

for line in open(file2,"r") :
    elements = line.strip().split("\t")
    if elements[0] in IDs :
        print "%s\t%s" % (elements[0], elements[1])

What I wrote above is a total hack, but something along those lines would work.

The following R script should do what you want:

#!/usr/bin/Rscript
args <- commandArgs(TRUE)
accession <- read.table(args[1], sep="\t", header = F)
tab.file <- read.table(args[2], sep="\t", header = F)
row.indices <- which(tab.file[,1] %in% accession[,1])
write.table(row.indices,file=args[3],quote=F,row.names=F,col.names=F)

just call it with:

./extract.R accession.txt tabular_file.txt out.txt

of course, you should have R installed, and you should not use this if your files are big ("big" depending on how much RAM do you have).

Change the flag to

grep -Fwf accession.txt tabular_file.txt > result