How strange. I had in mind to post this question since september, but did it finally today, finding two hours later a fresh email on a new study from Germany, with the most comprehensive data I have seen so far! It is bird data dominated, but also shows data on amount of agricultural surface since the 1950's and separated for different grassland types. For wet meadows abundance of each typical plant species is given for 1980 and 2008. The report also shows proportions of different crops since the 1950's. And much more. In German:

http://www.michaelottostiftung.de/de/presse/left-area/04/text_files/file/mos015_Studie_RZ_140618_lowres%202.pdf

http://www.michaelottostiftung.de/de/presse.html

Of course, I am still looking for species lists and abundance indicators of plant growing with certain crops, but this is a first relevant resource update to this question.

Jeroen, are you aware of and / or have you considered the Broadbalk weed data from the UK?

http://www.era.rothamsted.ac.uk/index.php?area=home&page=index&dataset=4

Thank you very much for the useful hints. I was not aware of the key term "weed shift". The key references on the weeds section of the Broadbalk site were also helpful. I never thought it would go back to 1867! Hints for Pre-1950's studies on weed shifts are of course welcome too!

Change in cropping patterns/Herbicide usage may result in weed shift.

An example: Weed Scandix pecten-veneris

Liopa-Tsakalidi A. (2014).Scandix pecten-veneris L.: A wild green leafy vegetable. Australian Journal of Crop Science 8(1):103-108 (2014). http://www.cropj.com/liopa_8_1_2014_103_108.pdf

you might be able to find historical records of herbicides applied or purchased in a given region then explore the relationship between herbicide use and weed abundance. That might be useful in some applications. 

Here is a recent study that takes place at the field-scale, of the effect of forest proximity to soya bean fields on pest regulation (and several other ecosystem services): 

Forest fragments modulate the provision of multiple ecosystem services (http://onlinelibrary.wiley.com/doi/10.1111/1365-2664.12241/abstract)

Thank you for the answers.

More specifically, I am looking for general trends in plants in agriculturally used fields since 1900 (or even 1800). I am especially interested in abundance of those plants providing pollen and nectar to pollinators, since I work with wild  bees. Pollination ecologists, are interested in the changing "pollinator landscape". What the effect of insecticide A or herbicide B in crop X is, does unfortunately not tell me anything about general trends, especially when no information is provided how widely it is and was applied and what long term effect are on the herb composition.

Nevertheless, I found some starting points and the supplied papers are also little pieces of the puzzle. I think there are multiple gaps in our knowledge to be filled, and many reviews possible depending on the focus. I do not feel offended when one of you feels the need to fill one of the gaps without noticing me.

For those following answers to this topic, I found following papers very helpfull:

Meyer et al. 2013 - Dramatic losses of specialist arable plants in Central Germany since the 1950s60s

Baessler & Klotz 2006 - Effects of changes in agricultural land-use on landscape structure and arable weed vegetation over the last 50 years

Andreasen et al. 1996 - Decline of the flora in Danish arable fields

Fried et al. 2009 - Arable weed decline in Northern France Crop edges as refugia for weed conservation

Moss & Storkey 2004 - The Broadbalk long-term experiment at Rothamsted: what has it told us about weeds?

Warington1924 - The influence of manuring on the weed flora of arable land

Sutcliffe & Kay 2000 - Changes in the arable flora of central southern England since the 1960s

That is a very interesting topic, surely there must be some changes but many factors are involves like coevolutionary, allelopathy  etc maters. The high chemical pressure and also recent GM are most important recent factors as of 1950s

An example from the US is Amaranthus palmeri, a native to the American Southwest but now an invasive agricultural weed in the midwestern US. See https://www.extension.purdue.edu/extmedia/WS/WS-51-W.pdf 

and Sarah M. Ward, Theodore M. Webster, and Larry E. Steckel (2013) Palmer Amaranth (Amaranthus palmeri): A Review. Weed Technology: January-March, Vol. 27, No. 1, pp. 12-27.

In California we use old local floras and weed manuals that were written at least 30 years ago, and compare areas covered in the old books with today's occurrences.  

Also our California Department of Agriculture in the 1950s and 1960 used to map Statewide the weed occurrences on a township and range scale, then estimate the acres covered within each township, so that is the most accurate maps available.  

Another method could be to visit herbaria and get the data from the sheets for each species that you are interested in.  Using that method, I was able to track how the Big Rattlesnake grass (Briza) was introduced and about what date, and how it spread from the original introduction around Monterey, for example.  

The work at Rothamsted in the UK would be of relevance.

For example:

Weed Science

September 2004, Vol. 52, No. 5, pp. 864-873

Symposium The Broadbalk long-term experiment at Rothamsted: what has it told us about weeds? Stephen R. Moss, Jonathan Storkey, John W. Cussans, Sarah A. M. Perryman, and Michael V. Hewitt  (doi: 10.1614/WS-04-012R1)