Sources: Reuters, Variety, RDI, The Hollywood Reporter, official studio press releases, and many others!

 Data updated as of September 2014

Note, however, that the estimations for the TOS films are *very* conservative.
Plus, foreign box office is difficult to obtain for most of the TOS films, and may be very underestimated.

Unadjusted Box Office Ranking
This is the most INACCURATE comparison of the box office success of each film.
NOTE: These figures are NOT adjusted for inflation.
See further down this page for the box office after inflation adjustment.

Movie	Domestic Gross	Foreign Gross	Total Worldwide Gross
1. Star Trek Into Darkness (2013)	$228,778,661	$238,602,923	$467,381,584
2. Star Trek (2009)	$257,730,019	$127,950,427	$385,680,446
3. Star Trek: The Motion Picture (1979)	$112,000,000*	$63,000,000*	$175,000,000*
4. Star Trek IV: The Voyage Home (1986)	$109,713,132	$37,287,868	$147,001,000
5. Star Trek: First Contact (1996)	$92,027,888	$54,000,000	$146,027,888
6. Star Trek: Generations (1994)	$75,671,125	$42,400,000	$118,071,125
7. Star Trek: Insurrection (1998)	$70,187,658	$42,400,000	$112,587,658
8. Star Trek II: The Wrath Of Khan (1982)	$78,912,963	$23,166,295	$102,079,258
9. Star Trek VI: The Undiscovered Country (1991)	$74,888,996	$22,000,000	$96,888,996
10. Star Trek III: The Search For Spock (1984)	$76,471,046	$15,222,150	$91,693,196
11. Star Trek V: The Final Frontier (1989)	$52,210,049	$19,009,966	$71,220,015
12. Star Trek: Nemesis (2002)	$43,254,409	$24,058,417	$67,312,826

* During the era of Star Trek: The Motion Picture, the weekly box office charts on Variety only covered the big cities and not the whole nation.
The national box office was only reported in some articles and only the first few weekends for each movie.
That's why even boxofficemojo.com only has the first few weekends for Star Trek: The Motion Picture, and it actually earned much more than the $82,258,456 claimed on that site.
This Variety method was changed to the more accurate method around the Wrath of Khan era of 1982.
The general consensus is that Star Trek: The Motion Picture earned about $175 million by summer of 1980. However, exact figures are difficult to obtain.

Trek Film Budgets
NOTE:  Mileage may vary.
These numbers are not adjusted for inflation.  
The budgets shown do not include advertising budgets.

Movie	Budget
1. Star Trek: The Motion Picture	$35 million *
2. Star Trek II: The Wrath Of Khan	$12 million
3. Star Trek III: The Search For Spock	$18 million
4. Star Trek IV: The Voyage Home	$24 million
5. Star Trek V: The Final Frontier	$30 million
6. Star Trek VI: The Undiscovered Country	$27 million
7. Star Trek: Generations	$38 million
8. Star Trek: First Contact	$46 million
9. Star Trek: Insurrection	$70 million **
10. Star Trek: Nemesis	$60 million
11. Star Trek (2009)	$150 million
12. Star Trek Into Darkness	$190 million

* By Paramount's bookkeeping, Star Trek: The Motion Picture cost $44 million to make.
But remember, Paramount is including the costs of development of the unfinished Star Trek: Phase II TV series.
Much of the TV series elements were not used for the film itself. Only $26 million was spent on the film itself.
Most sources place the film's budget at $35 million when including the cost of the usable elements of Phase II.

** The initial budget for Star Trek: Insurrection was closer to $60 million.
But after last-minute reshoots, including a new effects-heavy finale, the final budget was $70 million.
Most sources have already included reshoots into the budgets of all the other Trek films.
Why some sources are not taking these reshoots into account for Star Trek: Insurrection is unknown.

Trek Film Box Office Ranking Per Year Of Release

This is based on what rank the Trek movie came in that particular year.   
For example, Star Trek: The Motion Picture came in 2nd place compared to all of the movies that were released in 1979 worldwide.

The films have been ranked based on worldwide gross and domestic gross.
This is a pretty good method of showing the respective Trek film's popularity within a given year.
Worldwide rank takes priority over Domestic rank in the order listing below.
In the event of a tie in Worldwide rank, the order is listed by Domestic rank.
In the event of a tie in both Domestic and Worldwide rank, the order is listed by total adjusted worldwide box office.

Film	Domestic Ranking	Total Worldwide Ranking
1. Star Trek: The Motion Picture (1979)	3rd	2nd
2. Star Trek IV: The Voyage Home (1986)	5th	6th
3. Star Trek II: The Wrath Of Khan (1982)	5th	6th
4. Star Trek III: The Search For Spock (1984)	8th	7th
5. Star Trek (2009)	7th	13th
6. Star Trek VI: The Undiscovered Country (1991)	15th	13th
7. Star Trek Into Darkness (2013)	11th	14th
8. Star Trek: Generations (1994)	15th	19th
9. Star Trek: First Contact (1996)	17th	21st
10. Star Trek V: The Final Frontier (1989)	24th	27th
11. Star Trek: Insurrection (1998)	27th	32nd
12. Star Trek: Nemesis (2002)	54th	73rd

Trek Films - Critical Consensus

This is the overall average of the top film critics' opinions of the Star Trek films.
Only critical opinions at the time of release are used here.
Source: Metacritic.com

If the ratings are tied, the top critic percentage numbers of rottentomatoes.com will be used for the order listing (but those numbers will not be used in the actual percentages listed below).

* Does not include The Director's Edition, which is generally considered to be an improvement.

Trek Films - Worldwide Box Office/Budget Ratio
None of these figures (budget OR box office) are adjusted
for inflation or rising ticket prices.  This keeps the ratio intact.
Also note that the ratio doesn't remove the profits that went to the theaters.
Nor does it include advertising budgets or post-theatrical profits.
This is merely a direct box office-to-budget ratio.

Movie	Total Worldwide Box Office / Budget Ratio
1. Star Trek II: The Wrath Of Khan	8.5/1
2. Star Trek IV: The Voyage Home	6.1/1
3. Star Trek III: The Search For Spock	5.1/1
4. Star Trek: The Motion Picture	5/1
5. Star Trek VI: The Undiscovered Country	3.58/1
6. Star Trek: First Contact	3.175/1
7. Star Trek: Generations	3.107/1
8: Star Trek (2009)	2.571/1
9: Star Trek Into Darkness	2.46/1
10. Star Trek V: The Final Frontier	2.374/1
11. Star Trek: Insurrection	1.61/1
12: Star Trek: Nemesis	1.12/1

Total Worldwide Grosses Adjusted For 2014 Ticket Price Inflation
Matinees and dollar theaters are figured into the estimates.

Movie	Domestic Gross	Foreign Gross	Total Worldwide Gross
1. Star Trek: The Motion Picture (1979)	$363,665,338	$204,561,752	$568,227,090
2. Star Trek Into Darkness (2013)	$229,341,462	$239,189,892	$468,531,354
3. Star Trek (2009)	$280,066,620	$139,039,464	$419,106,085
4. Star Trek IV: The Voyage Home (1986)	$241,014,023	$81,912,702	$322,926,725
5. Star Trek II: The Wrath Of Khan (1982)	$218,755,323	$64,219,491	$282,974,814
6. Star Trek: First Contact (1996)	$169,689,431	$99,570,136	$269,259,567
7. Star Trek: Generations (1994)	$147,540,591	$82,669,856	$230,210,447
8. Star Trek III: The Search For Spock (1984)	$185,487,805	$36,922,775	$222,410,580
9. Star Trek: Insurrection (1998)	$121,967,892	$73,680,171	$195,648,063
10. Star Trek VI: The Undiscovered Country (1991)	$144,975,135	$42,589,074	$187,564,209
11. Star Trek V: The Final Frontier (1989)	$107,181,839	$39,025,497	$146,207,336
12. Star Trek: Nemesis (2002)	$60,675,290	$33,748,038	$94,423,328

Ticket price adjustment data is from Market Data Research from the Motion Picture Association Of America.

 If you have information regarding adjustments to any of these figures, please EMAIL me and let me know.
Please state your source and where this source can be found.
A quote in a Trek book saying something vague like "Such-and-such Trek Film was the most successful" does NOT count as factual evidence.  
I need REAL NUMBERS to make the proper adjustments and alterations, if needed.
More accurate information on the foreign box office take for the TOS films would be most helpful, for example. 

 If anyone tells you that a certain film is the "most successful," point out that when adjusting for ticket price changes and/or for inflation (which is FAR more accurate), the changes are staggering!