Question: I have cell values spanning over several columns and I want to create a unique list from that range. How?

Thanks to Eero, who contributed the original array formula!

Unique distinct text values from range tbl_text, array formula in B13:

=INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), MATCH(0, COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1)), 0), 1) + CTRL + SHIFT + ENTER

Copy cell B13 and paste it down as far as necessary.

Unique distinct num values from range tbl_num, array formula in D13:

=LARGE(IF(COUNTIF(\$D\$12:D12, tbl_num)=0, tbl_num, ""), 1) + CTRL + SHIFT + ENTER

Copy cell D13 and paste it down as far as necessary.

Explaining array formula in cell B13

=INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), MATCH(0, COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1)), 0), 1)

The array formula has two parts. One part returns row numbers and the other part returns column numbers. Let us begin with the first part, returning row numbers.

Step 1 - Find new unique distinct text values

=INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), MATCH(0, COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1)), 0), 1)

COUNTIF(range,criteria) - Counts the number of cells within a range that meet the given condition

COUNTIF(\$B\$12:B12, tbl_text)=0

becomes

COUNTIF("Text", {"Apple","Banana","Lemon";"Orange","Lemon","Apple";"Lemon","Banana","Orange"})=0

becomes

{0,0,0;0,0,0;0,0,0}=0

becomes

{TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE}

Step 2 - Convert boolean array to row numbers

=INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), MATCH(0, COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1)), 0), 1)

IF(logical_test;[value_if:true];[value_if_false]) checks whether a condition is met, and returns one value if TRUE, and another value if FALSE

IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)

becomes

IF({TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE}, {2;3;4}-MIN({2;3;4})+1)

becomes

IF({TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE}, {2;3;4}-MIN({2;3;4})+1)

becomes

IF({TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE}, {2;3;4}-2+1)

becomes

IF({TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE}, {1;2;3}) and returns {1,1,1;2,2,2;3,3,3}

Step 3 - Extract smallest value in array

=INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), MATCH(0, COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1)), 0), 1)

MIN(number1,[number2])
Returns the smallest number in a set of values. Ignores logical values and text

MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1))

becomes

MIN({1,1,1;2,2,2;3,3,3}) and returns 1.

Step 4 - Part two, identify array values in current row

=INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), MATCH(0, COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1)), 0), 1)

INDEX(array,row_num,[column_num]) returns a value or reference of the cell at the intersection of a particular row and column, in a given range

INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1))

becomes

INDEX(tbl_text, MIN({1,1,1;2,2,2;3,3,3}), , 1))

becomes

INDEX(tbl_text, 1, , 1)) returns array {"Apple", "Banana", "Lemon"}

Step 5 - Find new unique distinct text values in current row

=INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), MATCH(0, COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1)), 0), 1)

COUNTIF(range,criteria) counts the number of cells within a range that meet the given condition

COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1))

becomes

COUNTIF("Text", {"Apple", "Banana", "Lemon"}) and returns {0,0,0}

Step 6 - Find a new unique distinct text value in current row

=INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), MATCH(0, COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1)), 0), 1)

MATCH(lookup_value;lookup_array; [match_type]) returns the relative position of an item in an array that matches a specified value

MATCH(0, COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1)), 0)

becomes

MATCH(0, {0,0,0}, 0) returns 1.

Step 7 - All together

=INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), MATCH(0, COUNTIF(\$B\$12:B12, INDEX(tbl_text, MIN(IF(COUNTIF(\$B\$12:B12, tbl_text)=0, ROW(tbl_text)-MIN(ROW(tbl_text))+1)), , 1)), 0), 1)

becomes

=INDEX(tbl_text, 1, 1) returns value "Apple" in cell B13.

Explaining array formula in cell D13

=LARGE(IF(COUNTIF(\$D\$12:D12, tbl_num)=0, tbl_num, ""), 1)

Step 1 - Remove previously extracted values above current cell with an array with boolean values

=LARGE(IF(COUNTIF(\$D\$12:D12, tbl_num)=0, tbl_num, ""), 1)

COUNTIF(range,criteria) - Counts the number of cells within a range that meet the given condition

COUNTIF(\$D\$12:D12, tbl_num)=0

becomes

{0,0,0;0,0,0;0,0,0}=0

becomes

{TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE}

Step 2 - Convert boolean values to numeric values

=LARGE(IF(COUNTIF(\$D\$12:D12, tbl_num)=0, tbl_num, ""), 1)

IF(logical_test;[value_if:true];[value_if_false]) checks whether a condition is met, and returns one value if TRUE, and another value if FALSE

IF(COUNTIF(\$D\$12:D12, tbl_num)=0, tbl_num, "")

becomes

IF({TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE}, {1, 2, 1;2, 4, 3;1, 3, 1}, "")

becomes

{1, 2, 1;2, 4, 3;1, 3, 1}

Step 3 - Convert boolean values to numeric values

LARGE(array,k) returns the k-th largest row number in this data set.

=LARGE(IF(COUNTIF(\$D\$12:D12, tbl_num)=0, tbl_num, ""), 1)

becomes

=LARGE({1, 2, 1;2, 4, 3;1, 3, 1}, 1) returns 4 in cell D13.

Unique-distinct-values-from-multiple-columns-using-array-formulas.xls
(Excel 97-2003 Workbook *.xls)

ROW(reference)
Returns the rownumber of a reference

ROWS(array)
Returns the number of rows in a reference or an array

COUNTIF(range,criteria)
Counts the number of cells within a range that meet the given condition

IF(logical_test,[value_if:true],[value_if_false])
Checks whether a condition is met, and returns one value if TRUE, and another value if FALSE

MATCH(lookup_value,lookup_array, [match_type])
Returns the relative position of an item in an array that matches a specified value

INDEX(array,row_num,[column_num])
Returns a value or reference of the cell at the intersection of a particular row and column, in a given range

LARGE(array,k)
returns the k-th largest row number in this data set.

MIN(number1,[number2])
Returns the smallest number in a set of values. Ignores logical values and text

This blog article is one out of thirteen articles on the same subject "unique".

External resources:
Identifying Unique Values In An Array Or Range (VBA function)