(I can't speak for other armies but) the last time a British colour was carried on the battlefield was at the Battle of Laing's Nek on 28th January 1881, where the colour party of the 58th Regiment of Foot was present. The practice of bringing the regimental colours into battle was regarded as increasingly questionable as the 19th Century wore on and the old linear close-order formations became gradually more obsolete, but the 1877 "Field Exercise and Evolutions of Infantry" manual confirmed the practice. The wisdom of this was called into question shortly afterwards at the Battle of Isandlwana in 1879, where the 24th Foot lost three colours (Queen's Colour of 1/24th and both colours of 2/24th), and again at the Battle of Maiwand in 1880 where two colours of the 66th Foot were lost. In both cases lives were lost trying fruitlessly to save the colours from capture. Finally at Laing's Nek in 1881 the colours ended up in a dangerous position and, once again, lives were lost in (this time successfully) saving them from capture. Questions were already being put to the Secretary of War about the wisdom of bringing colours onto the field before Laing's Nek and that battle decided the issue. A circular sent to all infantry regiments on 17th January 1882 ordered that "In consequence of the altered formation of attack and the extended range of fire, Regimental Colours shall not in future be taken with the battalions on active service."
The above of course only refers to the British infantry, who were the last arm to carry colours in the field: the cavalry had ceased to do so decades earlier and the artillery never did so.
Taking as my sources I. Sumner "British Colours and Standards 1747-1881 (2) Infantry" (2001) and M. Barthorp "The British Army on Campaign 1816-1902 (3) 1856-1881" (1988), both of course published by Osprey.
It's unofficial practice, but today it is not unheard of for unit COs to fly a small version of their unit's guide on (pennant) from the antenna of their vehicle. This is done out of unit pride, however, not for any practical benefit. The U.S. guide on does go where the unit goes, though, so space is always found for it in the unit even at war. It's usually left behind with the gear in the psupply truck.