How much radiation do nuclear physics experiments expose researchers to nowadays?

In the US, the NRC limits whole-body occupational exposure to 5 rem/year. Specific labs or employers may impose much lower limits on their workers. For comparison, a CT scan is about 1 rem, and natural background is about 0.2-0.7 rem. There is not really any typical dose for people working on experiments. Depending on what their work is and how the experiment is set up, someone could have a dose that is not measurably higher than background. Or their measured dose could mount to the level where they're warned that they're nearing their limit for the year, in which case they might have to find someone else to whom to hand off the task that's causing all the exposure.

According to the German Federal Office for Radiation Protection (BfS), the average occupational radiation exposure (in mSv per year) in the group “research” (19489 persons in 2016) in the last years was as follows.

0.37 (2007)
0.41 (2008)
0.36 (2009)
0.35 (2010)
0.33 (2011)
0.35 (2012)
0.30 (2013)
0.28 (2014)
0.26 (2015)
0.27 (2016)

These values are generally lower than in other groups (medicine, industry, nuclear, flight personnel, or radon workplace).

Note that the dose limit for workers of category A is an effective dose of 20 mSv per year, averaged over defined 5 year periods (100 mSv in 5 years), with the further provision that the effective dose must not exceed 50 mSv in any single year. Nevertheless, the radiation exposure should be as low as reasonably achievable.

In 1990 de International Commission on Radiological Protection (ICRP) recommended the following radiation dose limits to workers and to the general public:

• 100 mSv in 5 years of effective dose for workers (maximum 50 mSv in any single year, average 20 mSv per year) of any branch, including medicine, industry, research, etc.
• 1 mSv per year to the general members of the public;

These recommendations have been implemented with minor changes into regulations in most countries, including the US and the European countries.

Radiations workers are obliged to use a personal dosimeter to record the amount of radiation they are exposed to. In my particular experience, most of workers don’t get more that 5 mSv in a single year, unless a radiation incident has occur, that’s why values higher than that used to be investigated. In fact I would investigate any reading in a particular workers dosimeter above the natural background.

The 1990 recommendations of ICRP have been recently updated, with almost no change to these values.