I am aware of h-index. I was wondering what other types of scores are both widely and rarely used to measure the impact of a scientist?
The h-index is common (and the g-index, which corrects for self-citation), as is the Journal Impact Factor. Johan Bollen has a good review of the various metrics.
However, it's important to point out that all those measures are just different ways of counting citations. They don't account for things like code you've written or talks you've given and they can't address systematic bias in citation practices such as coercive citation or citation mutation. Also, any citation-counting metric will penalize younger researchers simply due to the time it takes to publish one paper and for other papers to get published citing yours. In order to keep academics from having to publish a paper just to describe some code they've written or a dataset they've accumulated, aggregators have been built to pull in these various metrics and consolidate them. Total Impact is a good example of such a system. The general field of study looking at incorporating these broader metrics is called #altmetrics, and you can find a collection of research on the topic here.
Beyond the h-index, I don't think there's any definitive parameters used in practice. However, some other common factors used to evaluate research faculty:
- Publication count
- Quantity of funding
- Number of invited talks & invited journal articles
- Lab size
Note that these apply to the fields I'm familiar with, neuroscience and engineering. I suspect that these answers will vary according to field.
Take a look at this open article in Scientific Reports for a measure that attempts to discard productivity as a factor in evaluating the output of research.
I believe the answer to your question depends very strongly on the field. In mine, mathematics, the most used quick proxy for quality of research is the prestige of journals one's publishes in (which is not measured by impact factor, although there is a correlation).
In some humanities fields, books are the most prominent research outputs.
For a PhD student in biology (especially molecular and cellular, at least in some labs in France), time spent in lab in the evenings and week-ends seems to overweight everything else.