Looking around the fleet, I notice that a lot of people seem to quite enjoy dressing up their companions, purely based on the amount of Elaras, Kiras and Nadias that I see running around in bikinis. I have to admit that for me, this has never really been a priority. I want my characters to look reasonably presentable, but it's hard enough to keep on top of my own fashion and stats while levelling; I don't need to add to that by worrying about my companions as well (even if they do often end up looking like freaks in cut scenes, especially when the "hide head slot" option fails). At max level I tend to just give them hand-me-downs and spare raid or commendation gear, but I tend to not be too worried about their looks as they only come out for the occasional daily run anyway. (PvP? No companions. Ops? No companions. Flashpoints? No companions, assuming you run with a full group.)
However, as I've been playing my inquisitor lately, something started to nag at me. I've been spending an unusually high amount of time questing at max level with her, which means that I got to see a lot of my companions. Specifically, the ones that I used the most were Ashara, who is a (fallen) Jedi, and Andronikos, a pirate. All the gear that I put on the former made her look like a Sith, and all the gear that I put on the latter made him look like an Imperial agent. Basically, they both looked like exactly the opposite of what they actually are. So wrong!
Unfortunately my options seemed pretty limited at first. All regular and custom gear looks appropriate for your faction's classes, never the opposite faction. The exact same nice Jedi robe will turn into a Sith outfit if you send it over to an Imperial alt. The only items exempt from this are certain social items and gear from the Cartel market. I sure as hell wasn't going to spend real money just on dressing my companions!
Fortunately a brief look on the GTN soon revealed that things weren't nearly as dire as they appeared. Thanks to the Cartel packs, people end up with all kinds of undesirable adaptive gear that they then try to sell on the GTN for cheap. And even if it's not an outfit that you would choose for your own character, I found that a lot of it can make for a pretty decent companion look, especially with the addition of some dye. You don't need to gear them too thoroughly either, just a couple of pieces in key slots can do wonders.
For example I only picked up the following pieces for Andronikos:
Organa Statesman's Coat (dyed deep red/dark purple)
Rist Statesman's Trousers
The coat is really a bit frilly for a pirate to be honest, but at least he doesn't look like he just deserted from the Imperial army anymore. It's a fairly neutral look.
For Ashara I ended up buying a couple of pieces that all come in terribly garish and mismatched colours, but one dye module application and colour match later, it all suddenly works and she actually looks vaguely Jedi-like again. Success!
Ulgo Statesman's Coat (dyed deep red/dark blue, to match her skin)
Genteel Dress Gloves
Genteel Dress Bottoms
Organa Statesman's Boots
And the best thing? All of these items cost me less than 10k credits each (on my server anyway, your own might have different cheap options), most of them even less than 5k, with the exception of the dye kits, on which I "splurged" about 20k a pop. Maybe dressing up your companions to make them look vaguely presentable doesn't have to be an entirely terrible idea after all.