Seasons 1 and 2: Whole TV episodes skipped, transformation sequences altered, other video edits, OPs and EDs changed, multiple video and dialog changes to remove content deemed objectionable or unsuitable to North American audiences, sex of one character changed, and name changes.
Seasons 3 and 4: The dub for these two seasons are not as heavily edited as the first two were by DIC, but do contain significant changes from the orignal.
Movies: Pioneer has released edited VHS dubs, uncut VHS subs and uncut dub/sub DVDs.
DETAILED REPORT

Seasons 1 and 2: DIC andADV
Seasons 3 and 4: Cartoon Network and Optimum Productions and Pioneer
Season 5: Not yet translated into English by any company.
Movies: Pioneer

Seasons 1 and 2 (edited dub-only DIC release): The edited dub-only North American release of the first two seasons had such extensive changes that many story elements and characters were vastly different from the original.

Season 1 and 2 (subtitled ADV release): The missing previews frequently were very funny in their own right and added info not found elsewhere.

Season 2 (subtitled ADV release): Needless to say, the missing episode completely removes that episodes story and plot from the second season.

Seasons 3 & 4 (edited dub): The edited dub wasn't as bad as the edited dub for the first two seasons, but contained many changes which altered the story and plot.

Movies: No impact on story/plot except for some parts of the English dub.

Seasons 1 and 2 of TV Series (edited dub-only DIC release - released on DVD by ADV):

Japanese episodes 2, 5, 6, 20, 42, and 67 were skipped completely and were never dubbed into English.

Japanese episodes 45 and 46 (season one ending) were heavily edited to remove the deaths of Sailor's Mercury, Venus, Mars, and Jupiter. Instead they were 'captured' by the negaverse. Other edits shortened the running time and removed scenes of violence and blood.

Many scenes involving cars and busses driving on the left side of the street were reversed or other wise altered to make the cars or buses appear to be on the right side of the street (this despite the show being identified as taking place in Japan). Note to Sailor Moon dub watchers: If you ever go to Japan and drive on the roads, make sure to drive on the LEFT side of the road or you'll kill someone.

Many Japanese signs were altered and changed into English.

The transformation sequences were altered to remove internal lines that apparently looked too feminine for DIC. In my opinion, the shimmering effect was also intensified to make the transformation look less 'nude' (although some people disagree on this point, so it's just speculation on my part). Despite what some rumors have led some people to believe, the original transformation sequences were never 'nude'. The shimmering was always there and only the outline of the body was shown (no nipples or other sexual features were drawn in).

Various scenes of violence (including slapstick) were removed as well as shots showing under the scout's skirts (which appears to be just a continuation of their tops and not panties, in my opinion).

Sailor Says segments added to give some sort of moral to each episode (even if it had nothing to do with the story in the episode).

Seasons 1 and 2 of TV Series (subtitled ADV boxset releases):

Due to the materials not being provided, the next episode previews were not included on either ADV boxset and episode 67 was not included on the season 2 Sailor Moon R boxset. The 'today on Sailor Moon' previews for each episode were placed after each episodes' opening credits instead of before as it was originally.

Seasons 3 and 4 of TV Series:

These two seasons are not as heavily edited as the first two were by DIC, but there are still many changes (Sailor Neptune and Uranus are cousins instead of lesbians and references to the 'Mesiah' are removed, for instance). Unfortunately, while the Pioneer 'uncut' release is uncut video wise, the dub retains most, if not all, of these dub changes. The Pioneer DVDs also do not include the next episode previews for any of the episodes.

Season 5 of TV Series:

Not yet translated into English.

Movies:

The Sailor Moon R Movie dub VHS tape was edited for violence, some nudity, and the opening segment on the bus was replaced with a generic opening (which is used on all three movie releases).

The Sailor Moon R Movie sub VHS and dub/sub DVD had one short sequence at approximately 50 minutes 12 seconds into the movie where several seconds of reversed footage of Usagi's mouth moving was edited into the video. Reportedly, this was in the original theatrical print Pioneer was provided and latter fixed for the home video release in Japan.

For more detailed information on the changes to Sailor Moon, please see Ken Arromdee's extensive Sailor Moon FAQs available at http://www.rahul.net/arromdee or Sailor Moon Uncensored at http://smuncensored.com.

Seasons 1 and 2 of TV Series (edited dub-only DIC release - released on DVD by ADV): Completely different OPs was assembled from various sources. ED was mostly intact.

Seasons 1 and 2 of TV Series (subtitled ADV boxset releases): Only one of the openings was used for all episodes in the season 1 boxset, instead of the unique openings that added the sailor senshi as they joined the show.

Seasons 3 and 4: Cartoon network did not use the original OP and EDs. The Pioneer 'uncut' home video release contains the original endings, but doesn't contain the next episode previews and only uses one of the many different opening variations.

Movies: Completely different OP was assembled from various sources and used for all three movies on the edited dub VHS release. Sub VHS and dub/sub DVD contained the original openings.

Seasons 1 and 2 of TV Series (subtitled ADV boxset releases): No edits reported (although ADV did choose to translate Sailor Senshi as "Sailor Warriors" instead of the more commonly used "Sailor Soldiers").

Seasons 3 and 4 TV series: No edits reported.

Movies: No edits reported.

Too many to mention them all, but many changes revolve around: names, many of the attack names were changed, the initial "... Power, Make-up!!" transformation cries were changed to drop the 'make-up' potion, the homosexual relationship of Zoisite and Kunzite, Michiru and Haruka relationship, violence, Artemis' crush on Luna, and other various changes to make the dialog acceptable to North American audiences.

Seasons 1 and 2: Many dialog changes were made, including changing the sex of one character.

Season 3 and 4: Sailors Neptune and Uranus are now COUSINS instead of being lesbians, references to the Apocalypse and Messiah altered and changed. Unfortunately, while the Pioneer 'uncut' release is uncut video wise, the dub retains most, if not all, of these dub changes and can't be considered UNCUT.

Movies: Various changes to dialog that is inconsistent with the subtitles and original dialog.

A quick breakdown of some of the name changes for the English dub:

Sailor Moon/Usagi became Serena in the English dub
Sailor Mercury/Ami became Amy in the English dub
Sailor Mars/Rei became Raye in the English dub
Sailor Jupiter/Makoto became Lita in the English dub
Sailor Venus/Mina became Mina in the English dub

Sailor Neptune/Michiru became Michelle in the English dub
Sailor Uranus/Haruka became Amara in the English dub

Mamoru became Darien in the English dub
Chibi-Usa became Rini in the English dub

Zoisite became Zoycite in the English dub (plus he became a very flat chested woman)
Kunzite became Malachite in the English dub
Queen Metallia became the Negaforce in the dub

Dark Kingdom became Negaverse in the English dub
Earl (pronounced ail in Japanese) became Alan in the dub
Kooan became Catzy in the dub
Beruche became Bertie in the dub (apparently meant to be Birdy)
Calaveras became Avery in the dub
Petz became Prizma in the dub

• Currently the only way to get the complete and uncut Sailor Moon TV series is by obtaining an import version from Japan (should be available on SVHS, LD, DVD, and VCD from various sources).