There are no 1790 or 1800 Federal Censuses for Kentucky, so tax rolls are an alternative.  It was not necessary to own land to be on the tax rolls, one could be taxed on the ownership of horses or slaves, and white males over 21 were taxed just for existing!  However, citizens were sometimes exempted from taxes.  The aged and infirm were often exempted as were widows with small children.  And it appears that sometimes exemptions were granted for community service of certain kinds.  So while death and taxes were/are inescapable, and the tax rolls are probably more complete than the census, even the tax rolls are not 100% complete.  (Aged men were also exempted from road-building.  A reading of the county court order book shows that as part of their civic duty, male citizens and their slaves were ordered to render a great deal of service to the county in the form of road-building.  Some of this service may have led to exemptions from county taxes.)

I've extracted the following from microfilm of the Christian Co. tax rolls (Heritage Quest Microfilm, V20-72).  This microfilm is of the county record book, not the original tax lists.  Names from the individual tax lists were roughly alphabetized, then entered into the book, usually by the county clerk and usually giving the date the list was received by the clerk.  So, while we've lost the potential ability to find "neighbors," I think there is some reason to believe that individuals who lived in the same watershed and whose list was received by the clerk on the same day were living in greater proximity to one another than those whose list was received on a different date.  Anyway, it's something to go on...
 

For detailed lists, CLICK HERE:

1797-1803

1804-1809

1810-1813

1814-1816

For a quick summary:
 

THOMPSONS on Early Christian Co. Tax Rolls (extracted by DGM)
1797		John
1798		James, Joseph
1799	1	James, Joseph, John, Robert
	2	James, Joel, John, Peter
1800		James, Joel, John, Peter
1801	N	James, James Jr, John Sr, John Jr
	S	Joel, Peter
1802		James, Joel, John, Peter, Samuel, William
1803		Adam, James, James, Joel, John Sr, John Jr, Nicodemius, Peter, William
1804	N	Adam, James Sr, James Jr s/o James Sr, James S?, James Jr, John Sr, John Jr, Sarah, William
	S	Joel, Peter
1805	N	Adam, James, James, John Sr, John Jr, Samuel, William, __?__
	S	Joel, John, Peter
1806	N	Adam, James, James M., James Sr, James Jr, John Sr, John Jr, Samuel, William
	S	Joel, John, John, Peter
1807	E	James, James, John, John, Peter, William
	W	Adam, James M., Joel, John, John, John, John, Samuel, William
1808	1	James, James Sr, James Jr, John Sr, Peter, William
	2	Daniel, James, John, John, Richard, William
1809	1	Gideon, James, Cap John, John, Peter, William
	2

The tax rolls of Christian from 1804-1823 have been transcribed and self-published by A.B. Willhite in four volumes (1804-9, 1810-13, 1814-18, and 1819-23), available for sale from the Christian County Genealogical Society.  Unfortunately, the third volume (1814-18) is out of print.  (If anyone has a copy they are willing to sell, please contact me!)  Willhite's transcriptions are of the county record books, not the original tax lists.

From 1804 to 1809, Christian Co. was divided into two tax districts:  from 1804 to 1806, into  North and South districts; from 1807 to 1809, into East and West Districts.  Districts were abandoned, at least for tax purposes, in 1810.
 

THOMPSON on Christian Co. Tax Rolls, 1804-1809  (extracted by Willhite)
1804	N	Adam | James | James Jr | Jas Sr | Jas son of Jas Sr | Jno | Jno Jr | Sarah | Wm
	S	Joel | Peter
1805	N	Adam | James | James | Jas | John | John Sr. | Samuel | Wm
	S	surnames "R" thru "V" missing from book
1806*	N	p. 66:  Adam | James | James M | James Sr | James Jr | John Sr | John Jr | Samuel | Samuel | Wm |
		p. 65:  Joel | John | Peter
	S	p. 86:  Joel | John | John | John | Peter
1807	W	Adam | Jas M | Joel | John | John | John | John | Saml | Wm
	E	James | James | John | John | Peter | Wm
1808	W	Daniel | James | John | John | Richard | Wm
	E	James | James Sr | James Jr | John Sr | Peter | Wm
1809	W	Adam | James M | Joel | John | John | John | Samuel | Samuel | Thomas | Wm
	E	Gideon | James | John | John | Peter | Wm
*There appears to be some kind of corruption with the 1806 records in Willhite's book, with a block of records out of alphabetical order and in the North District that look as if they should be in the South District, some of which appear to be listed in both places.  Without seeing the original tax rolls or microfilm, I can't straighten this out.
SOLUTION:  I've just discovered that the records "missing" from 1805 are the ones "duplicated" in 1806!

For Thompson in earliest Todd Co. lists, CLICK HERE:

1820-1823

1824-1827

1828-1830

THOMPSON in 1840 Tax List - Todd County, Ky, Part 1 and Part 3 transcribed by Karen Combs.

Pg.	Name	Acres	Watercourse	Value
4	Burrus, Nathaniel, agent for Thos Thompson	260	Westfork	2000
31	John Thompson	137	Elkfork RR	274
46	Thompson, Ale?	196	Westfork	1370
46	Thompson, Robert?	189	Westfork	1320
46	Thompson, Sophia Sr	67½	Westfork	260
46	Thompson, Matthew	-	-	-
46	Thompson, Gideon	150	Elkfork	1200

"Ale?" is Alexander Thompson.  Matthew lived in Todd City (apparently did not own land).  Elk Fork and West Fork are tributaries of the Red River.

THOMPSON on 1845 Tax List - Todd County, KY, Part 1, in the process of being transcribed by Karen Combs.

Pg.	Name	Acres	Watercourse	Value
5	Burrus, Nattel, Agt for Peter Thompson heirs	260	Westfork	2600