Please be patient with my rambling, TheFixer, there's useful information scattered around, down there.
The black bars are normal for TNG, DS9, and Voyager episodes. Those DVDs (most/all seasons) were sourced from videotape.
[(pre?)broadcast masters].
Videotape doesn't have as wide of a picture as the DVD specifications. Both videotape & DVD have a wider picture than most fullscreen sets were designed to show. (See "Overscan" at the bottom of this post). And DVD specs were for a wider picture than videotape - it helps squish a widescreen movie on there, more easily. I believe most Dr. Who were videotape as well (except the Digitally-remastered DVDs), I think I've read that, and the few-thousand
episodes I saw on PBS looked like video (I haven't gotton around to buying the DVDs yet). (Off the subject, Laserdisc is also less wide than DVD, without refreshing my memory, I think its roughly the same as videotape). All the Treks were primarily film, but the crude early CGI methods, of the middle-three series-es, were output to videotape (at least in the earlier years). For some reason ($$$), they don't seem to have made digital scans of the film portions, for the dvds. (I haven't sussed out what they did for the later seasons of DS9 and Voyager, or for Enterprise, yet). But it could be worse - many television shows were pure videotape, which was bad for the DVD era and is much worse for the HD era.
Theatrical films, if you notice, don't have these black bars on the sides. Digitally-Remastered shows don't either. Neither does TOS, because it was pure film (But they zoomed in on the film, for the DVDs, as they did for broadcast prints, Laserdiscs, and videotapes. For instance, the "Trials and Tribbleations" source was zoomed out wherever possible. "But Troubles with Tribbles" is zoomed in a bit. Sometimes there would be a boom mike, cables on the floor, the side/top of the set would run out or other crap - so the cheap way, (the only way that film-for-television, could afford) was to just zoom in to avoid the worst-case problems, and leave it that way - like most productions do with open-matte versions of theatrical films - where they could afford to do it right).
Errr... but back to your question...
My advice would be to leave them as-is.
But you can crop the black bars off of the size and:
A) Also crop the top &/or bottom proportionality, and resize. This will make the picture a little fuzzier.
B) Crop the sides and resize horizontally. This will distort the picture slightly, make the people look slightly shorter and fatter, and fuzzy-up the image in one direction.
There's an aspect ratio calculator tool post sticky-ed up there, and ADigitalMan's Guide has a section on cropping and resizing.
More problems:
Tape-sourced NTSC shows, on PAL DVD's, have already, typically, been resized, so any further resizing will make things worse. Resizing doesn't recover lost detail, so things look more indistinct. You can use sharpening, but that'll bring on other kinds of artifacts. It's a slight resize, and it may look acceptable, but I'd avoid it.
It doesn't stop there - the black bars aren't always a consistant width, in the Trek episodes - you'd have to crop some shots separately.
And then there's the matter of scan lines being resized. That gets messy. You'd rather IVTC (Inverse-telecine - remove the extra fields inserted by telecining) (And not de-interlace, which throws away non-duplicated information), first, but the TNG/Voy/DS9 are a combination of soft-telecine ("pulldown flags" tell the dvd where to add telecine), 30-fps compositing, 24-fps telecined credits, viewscreen shots that appear to have 60-field videotape source and some other oddities. (Stargate is a much weirder mix, because any source can go into the CGI and the CGI can be 24 fps or 30 fps. The new BSG is said to be just as bad). I don't have the PAL versions, but I know the telecine situation is even screwier after a PAL conversion. So you'd have to note which ones were, for example, 30 fps, and keep the different types separated, to be sped up or soft-telecined. That'd be far too much work for a full episode (I'm doing it on a small scale in the relatively-simple NTSC versions, prior to some compositing).
[Here is where I spare you some off-topic stuff I originally typed. There were the observations I've make in my current project. A half-remembered online-ariticle on the PAL conversions, which had info directly from the source. A little-known tidbit that explains the NTSC scanlines in the transporter scenes. And some unanswered questions I have.].
Along with the TOS remastering, a TNG/DS9/Voy remastering is in the works, or at least rumored, for HD. I expect it probably wont make it to SD DVDs.
I don't know if they're going to butcher them into a 16:9 cropping, for HD.Overscan:
The original idea was to broadcast a wider picture than was meant to be seen, in case some televisions showed a wider picture than expected. Also, the phosphor dots, and the electron-beam that lights them, go to the edge of the picture tube - but the edges of the tube are hidden by a mask around the edges. That's in partly in case the broadcasters don't broadcast wide enough. Sigh. Or, actually, I don't know why they waste it. Computer monitors CRTs do that as well. The front rim holds the tube in place, but then why bother to put the dots out to the edge?
A few fullscreen CRT TV sets can have the width adjusted - but it requires a much more expensive (and heavy) variable-frequency high-voltage, high-amp transformer linked to other variable-frequency circuitry (Vertical sync is much easier, at a low frequency, so all sets have that). Some newer sets are designed to show the "overscan" area as well. LCD and Plasma are another kind of animal.
This means that most people, with fullscreen, aren't seeing the edges of ANY of their DVDs's/LDs's/Videotapes's picture... aggravating.
Computer monitors are tiny, and heavy, in comparison with typical large TVs, and much higher-tech in the first place, so they come with horizontal and vertical size adjustment. So you actually see the black bars, on monitors.
By the way, outside of Japan, NTSC's "black level" is actually slightly gray, I mean grey.
(Seriously, though, I can't keep the two sorted, I read both, when I was young, and got marked wrong by a teacher, in a spelling test, once, because they only accepted American spellings). So the black bars are pretty obvious on a computer monitor. But it should match the black on a properly-adjusted widescreen set... hmmm, I don't know what the black level is on PAL, but I assume that's all taken care of in the DVD specs, or whatever. The gr?y is particularly obvious on computer monitors, because computer monitors have a better gr?y scale and color-depth, than a Standard-Definition TV-signal can carry.