Most alien (or non-human of any kind) languages in media are simplistic and based on the language of the creators of the media. Provided the languages have some form of grammar established, be it languages from fantasy creatures or aliens, they will always look more like English than even Welsh looks like English. It seems that even when aliens aren't speaking English, they're speaking something like it. In the Con Lang community, these alien languages would be described as a "relexification" of English, or relex for short — many of these may count as fictionaries.
Some conlangs, however, go beyond that, and the author actually shows their work to some extent and creates a language with grammar that is different from that of English. Unfortunately, the result often still shows the typical features of Indo-European languages - similar inflection or conjugation patterns, similar use of copulae and auxiliary verbs, and so on.
As most writers are not linguists, this trope crops up unsurprisingly often across fiction. Of course, you would have to be extremely dedicated to create an entire language not based on your own at all — and even if you did, only the particularly dedicated would try to learn it. Thus, it follows that most fictional languages look like English, particularly from the perspective of native speakers of Basque, Turkish or Hebrew, for instance. Not that that's necessarily a bad thing though.
What really counts is how an author uses their Con Lang in story. A story with a Con Lang that shares few similarities with an Indo-European language will still fail if it's a bad story. And remember that as much as authors can try to avert this trope, similarities to other languages is not a bad thing.note and depending on how this Con Lang fits into your world, can be a very good thing And unless that particular Con Lang is going for The Unpronounceable, then all languages will share some very basic similarities.
If the author invents a language designed to avoid similarities to any real language, that falls under Starfish Language. Relex or relexification is something that happens when the invented language has what amounts to a one-to-one correspondence with the language the work is written in, and a Conveniently Precise Translation is the result.
Played straight with the Vulcan language in Star Trek: The Motion Picture, where, during the Kohlinahr ritual, the actors spoke English on set and were later overdubbed with "Vulcan" words that more or less matched their lip movement.
Mostly averted in Star Wars. People speak Basic (i.e. English) most of the time anyway, but Shyriiwook gets points for A: being just onelanguage of the Wookiees, B: being very different from English when we hear it and C: being so hard to learn, Leia has to get help from a Wookiee with a speech impediment that makes the language easier for her. Indeed, in the movies it's based on bear noises. Other languages spoken such as Huttese are based on the sounds of languages like Aymara and Quechua (neither of which are Indo-European), although Huttese is not a conlang, just a bunch of random sounds. And, to top this off, there's a lot of bilingual conversations in the Star Wars movies and EU, with the fairly reasonable justification that some species' vocal apparatuses simply can't make the sounds of the other languages.
Bright Tree Ewokese is based on Tagalog.
According to Wookieepedia, the language of High Galactic was the original language of the Republic and Jedi Order before Basic. Some of the words, like "fi" for son, or "pera" for father, suggest that it is a Latin/Romance language expy. Which makes sense, since the Republic lives and breaths the Space Romans trope.
Mando'a, the Mandalorian Language, gets a lot of flak for being pretty much a re-lex of English. Most of the criticism is deserved,note It's got the exact same phonemes (except for the voiced and unvoiced Th's, Z, and the sound in "vision") and the same rules for where they can occur (no "ng" initially, for instance); its whole structure is "analytic with a few fusional elements", just like English, e.g. it lacks cases and mostly just inflects verbs for tense (like English); and even the particular details are similar, like how its adjectival suffixes are "-yc" and "-la", which are respectively the My Nayme Is version of "-ic" and "-al" backwards. but the vehemence—the same can be said of almost every fictional language in almost every franchise's Expanded Universe—is probably part of the backlash against Karen Traviss and her Writer on Board treatment of the Mandalorians.
Inverted in Prometheus; according to it, our ancestors actually picked up Proto-Indo-European from the Engineers.
Even J. R. R. Tolkien fell into this despite his incredible dedication to his languages (he himself was a philologist). Quenya was originally based on Finnish grammar; however, Finnish is part of a language family called Uralic that is unrelated to Indo-European, but shares some similarities, and Tolkien negated any brownie points by removing all the parts of Finnish that made it so Uralic to start with. If we want to be didactic, the phonology was a mix of Finnish and Latin, morphology is totally Finnish, syntax is a mish-mash of Latin and Greek. Sindarin was based mostly on Welsh, a Indo-European language in the Celtic subfamily. Interestingly, he made a serious effort (and not too shabby of one either) to derive them from the same source language, even though this would be completely impossible for the languages they were based on.
Khuzdul (Dwarvish), and to some extent Adûnaic, have a triconsonantal root structure similar to Semitic languages (which aren't Indo-European, but the same applies). However, there is too little extant Khuzdul text to compare its grammar. (Tolkien actually wrote a good deal about the grammar of Adûnaic, but this troper doesn't know enough about any Semitic language to compare.) When linguist David Salo developed a more complete version of Khuzdul for the movies, he based the grammar mostly on Arabic, while most roots of the vocabulary come from Germanic languages (some more blatant than others).
In Artemis Fowl, the fairy language, including its writing system, amounts to a direct cipher of English, despite the fact that it's out right stated that the (very different from English) ancient Egyptians derived their language from the fairy language.
Despite being described as a very difficult to learn language, the High D'Haran from The Sword of Truth series seems to be that from the samples given.
Hardly comes into play, but K'Da language in Dragonback by Timothy Zahn is such. Because it is derived from proto-Indo-European.
V: The Series novel "East Coast Crisis" by Howard Weinstein and A.C. Crispin includes this description of Visitor writing : "To a human familiar with ancient Hebrew or Sanskrit the characters might have appeared faintly recognizable, but to anyone else they would have been totally indecipherable." A brief discussion of this with a comparison of Hebrew and Sanskrit characters can be found here : http://v.popapostle.com/html/episodes/V80/East-Coast-Crisis.htm
Leaving to one side that there's no such writing system as "Sanskrit", which was primarily a spoken language (everyone in India writes Sanskrit in their own writing systemnote The thing Westerners often call "Sanskrit" is actually Devanagari, the script used most notably by Hindi among other languages.), it probably means that Visitor only really writes the consonants, with the vowels rendered as diacritics.note Indic scripts, called "abugidas", have a default vowel, usually "A", and change or delete it with diacritics. Semitic scripts (aside from Ethiopian, which is an abugida) are "abjads", and write all their vowels, if at all (they're often omitted if they're clear from context), either by diacritics or by repurposing a consonant—W often stands in for long U in Arabic, for instance. Of course, just because an alien script works like a script you know doesn't mean you'd recognize anything about it. (Glagolitic, for example, works just like our alphabet, and it actually is related to it—but how much of it do you recognize?)
Live Action TV
Star Trek, at times when the Universal Translator still fails. All alien languages sound as if they obey English phonology, but their transliteration to the Latin Alphabet seems extremely implausible, using c and k interchangeably and the obligatory useless apostrophes.
Dominionese apparently has a passive voice transitive which serves as an optative mood. In other words? Basically, if they weren't just selecting linguistic terms from a hat, the inhabitants of the Dominion make much more use than English does of idioms where, e.g., "You're murdered" means "I wish you were dead" (presumably when a Vorta wants you to have a nice day he says "You're well-treated", for example).
The Twilight Zone episode "To Serve Man" runs into this a bit, first because the Kanamit alphabet has uppercase and lowercase letters (other languages have multiple variants—e.g. Japanese hiragana and katakana—but use them differently; hiragana is for normal writing and katakana is basically italics, used for writing foreign words), and second because most languages don't have an idiom where "serve" means "prepare as a dish".
In the Stargate Verse, the Ancient language is literally this trope. It's a close ancestor of Latin. Which means that somehow (time travel?) it must be descended from Proto-Indo-European.
The Ilithyrii, Darkelf or better known as Drow language is just basic English grammar (plurals end with n instead with s, female titles still end in-ess, etc) with new words based on a lot of hissing sounds (sibilants) like x and s to simulate their underdark home that's prone to echo "harder" consonants a lot.
Played with in World Tree RPG. The world's languages are based on a divinely created Common language with simplistic grammar, and all known languages are based on Common. So every language in that setting is like this trope towards every other, and described as being only about as different as English and Italian (ie. not very). We're also told that the standard pronoun "genders" are based on species, so that "the male Cani greeted the female Rassimel" would be written as something like "Ce greeted rir" instead of "He greeted her". The in-character journal by one of the game's authors has the hero dealing with other grammatical oddities like social-class markings, and even making fun of cheap in-universe novels that don't think through their "alien" language.
The First Tongue from Werewolf: The Forsaken, the language of the spirit world. Given its name, however, it may be justified. The developers even admitted they've come up with terms for it by going down the Indo-European language tree and taking a few turns.
The Dragon language in The Elder Scrolls V: Skyrim is basically a relexification of English—except without tenses, since the dragons who speak it are timeless beings; what look like tense-constructions are usually either aspect or passive-voice. Its script was invented from scratch—it's cuneiform-esque, based on scratches made with dragon-claws.
In the other Elder Scrolls games, the daedric language is simply English spelled with a unique script.
Al Bhed in Final Fantasy X, which uses a simple substitution cipher but is apart from that identical to English.
This was a criticism made of the "Martian" language of the "messages" produced by 19th-century medium Hélène Smith via automatic writing — it bore a considerable resemblance to her native language, French.