which travel company had the following slogans:

1.  If....don't do it, don't do it
2.  It's not all sex, sex sex.

Dear cypic-ga,

The first one slogan was for Thomson Holidays (a UK travel company).
The full slogan is quoted to be: "If Thomson don't do it, don't do it.
But if they do, do."

Sources:
"The Art and Science of the Advertising Slogan" Section 10
http://www.adslogans.co.uk/ans/adslogans_artscience.pdf

The Independent, Sunday (UK), April 30, 2000 p19
"Britain's biggest holiday company, Thomson, used to have the slogan
"If Thomson don't do it, don't do it". Thomson does most things these
days, having bought companies such as Austravel, and expanded its
customers' horizons from Turkey to Thailand."
(I cannot refer you to the original article as I accessed it through
an account I have with an online news database. The article does not
appear on the Independent's archive http://www.independent.co.uk)


The second slogan was that of Club 18-30 during a 1995 advertising
campaign (UK company).

Sources:
"The Saatchi & Saatchi ads generated 490 complaints centred on posters
featuring the taglines "Beaver Espana" and "It's not all sex, sex,
sex. There's a bit of sun and sea as well"."
http://news.bbc.co.uk/2/low/business/3163077.stm

Advertising Standards Authority - Adjudication - Page 9 
http://www.asab.org.uk/NR/rdonlyres/0EEDC7F5-3913-4E29-AFCA-025574B0190B/0/ASA_Statistics_1995.pdf


I hope this answers your question. If it does not, or the answer is
unclear, then please ask for clarification of this research before
rating the answer. I shall respond to the clarification request as
soon as I receive it.
Thank you
answerfinder

Succesful search strategy
"if * don't do it" slogan
://www.google.co.uk/search?hl=en&q=%22if+*+don%27t+do+it%22+slogan&btnG=Search&meta=
"It's not all sex, sex sex"
://www.google.co.uk/search?hl=en&q=%22It%27s+not+all+sex%2C+sex+sex%22&btnG=Search&meta=