Highest paid engineering jobs

Coparison of starting and mid-career median pay by occupation.
                                               Starting     Mid-career       
                                                       median pay     median pay
    Petroleum Engineering         $93,000        $157,000
    Aerospace Engineering         $59,400        $108,000
    Chemical Engineering         $64,800        $108,000
    Electrical Engineering        $60,800        $104,000
    Nuclear Engineering            $63,900        $104,000
    Applied Mathematics         $56,400        $101,000
    Biomedical Engineering         $54,800        $101,000
    Physics                     $50,700        $99,600
    Computer Engineering        $61,200        $99,500
    Economics                    $48,800        $97,800
Source: Engineering Employment and Earnings Outlook  By Ilya Leybovich, February 15, 2011

In generally how much do engineers make, From the same source, the expected employment growth in engineering in US through 2018 is 11%, from a base of 1.57 million as of 2008. The estimated growth by area is as follows:
Biomedical engineers: 72%
Environmental engineers: 31%
Civil engineers: 24%
Petroleum engineers: 18%
Mining and geological engineers: 15%
Industrial engineers: 14%
Agricultural engineers: 12%
Nuclear engineers: 11%
Aerospace engineers: 10%
Health and safety engineers: 10%
Materials engineers: 9%

From an updated report we could see some of top paying engineering jobs:
OCCUPATION   2020  MEDIAN PAY      
Petroleum Engineers   $130,280     
Nuclear Engineers   $104,270     
Aerospace Engineers   $103,720     
Computer Hardware Engineers   $100,920     
Chemical Engineers   $94,350     
Electrical and Electronics Engineers   $89,630     
Marine Engineers and Naval Architects   $88,100     
Biomedical Engineers   $86,960     
Materials Engineers   $85,150     
Mining and Geological Engineers   $84,320     
Environmental Engineers   $80,890
Mechanical Engineers   $80,580     
Civil Engineers   $79,340     
Industrial Engineers   $78,860     
Health and Safety Engineers   $76,830     
Agricultural Engineers   $74,000     
Architects   $73,090
Landscape Architects   $64,180
Bureau of Labor Statistics, U.S. Department of Labor, Occupational Outlook Handbook, 2014-15 Edition, Petroleum Engineers, on the Internet at U.S. Bureau of Labor Statistics (visited June 13, 2015).

If you are interested how the starting salary has been changing through time, Lynn L. 2011 et al's work could give some info:
Petroleum (B.S.) Engineers Starting Salaries
Year    Starting salary
1997    $43,674
1999    $50,400
2003    $55,987
2005    $61,516
2010    $86,220
Source: Lynn, L., Salzman, H., & Kuehn, D. (2011, September). Dynamics of Engineering Labor Markets: Petroleum Engineering and Responsive Supply. In conference paper presented at “US Engineering in the Global Economy”, sponsored by the Alfred P. Sloan Foundation and the National Bureau of Economic Research. Petroleum Engineering and Responsive Supply

And if you are interested to know how your salary could be increased with a master or PhD degree, this could help you:
In 1992, nonsupervisory engineers with masters degrees made an average of about $6,000 more per year than engineers at the bachelors degree level. The Ph.D. premium--the salary differential between those engineers holding doctorates and those with masters degrees--was about $10,000. 
Engineers with supervisory responsibilities make an average of about  $20,000 more per year than those without supervisory responsibilities.
Source: Science & Engineering Indicators

If you are a woman and you want to know if there is a salary difference by genere, this is an example:
Estimate and median salary of full-time workers with highest degree in S&E field, by sex and occupation: 2010
Occupation                        Number      Median salary ($)
Total Petroleum Engineers        15,000         117,000   
Female Petroleum Engineers         2,000        115,000       
Male Peroleum Engineers         13,000        117,000