Providing video over the Web was an issue once plagued by a need for multiple proprietary plug-ins, some of which worked better than others, but the duty of playing video has now mostly passed to a single plug-in, Adobe's Flash Player, a method popularized by YouTube. The video "player" is actually a Flash file (whereas before it would be part of the plug-in), usually custom designed and coded by someone on the site's development team. It contains the DVD-like controls and also handles the way the video is sent to the browser. Unfortunately, this puts the burden of making a working player on the site developers, and some do not know how to do it correctly.
There are basically two types of Web Video sites, those that do it right, and those that don't. Actually there are probably three types: those that offer non-porn and do it right, those that offer non-porn and don't do it right, and those that offer porn, and do it right. Those that offer porn and don't do it right usually don't get people (e.g. paying customers) to stick around and thus they go bankrupt, so those sites tend not to last long.
One of the most important features is the ability to go forward in a video (to skip uninteresting or boring parts), but even more important is the caching of video. The Internet isn't always smooth delivery; sometimes you get a slow connection or the site gets hit by a lot of traffic. So the video is generally sent such that it runs a few seconds behind the image so that if it hits a slow signal, it can ride through it without the video jerking to a stop while it waits for more material to be sent. This process of sending video faster than you watch it is referred to as "caching" or "buffering." Most sites, in fact, continue to send the video even if you hit the 'pause' button, so that if your connection is slower than the speed of the video, you can pause the video, go away and do something else, and come back and eventually have all of the video available. Consider the idea of filling a large bucket from a (very) slow faucet; you might turn it on, walk away and come back later while the bucket fills, as opposed to using the water a little at a time.
A clear and obvious indication of a place that does not do it right is a player that does not cache. This means, if your Internet connection isn't absolutely flawless, video presentation is not going to work, and the video will operate on the basis of: play (for about a second or two); jerk stop and freeze with a spinning cursor, wait about 5-10 seconds for the signal to catch up; play a couple seconds; jerk; stop; play; jerk; play; etc. (If you've ever seen someone who's learning how to drive and doesn't yet know how to use the brake correctly, you'll get the idea.) Other sites do not use the buffer effectively; the player will show a growing bar showing how much of the video is loaded, with the spot you're currently watching a good distance behind, yet the video will still halt every few seconds to buffer some more, defeating the purpose of having a buffer in the first place.
If they're really stupid, they'll simply drop the frames that don't show up, so you get a second of video, then after four or five seconds when the feed catches up, the video skips forward 4 seconds, runs for a second or two, stalls, then resumes at that point a few seconds later in the video, dropping the part that couldn't keep up. This might be understandable if you were watching live streaming video, but we're talking about stored video being sent from a server; this sort of practice is not just bad, it's inexcusably bad.
Worse, some of the sites that don't cache, if you pause the video in order to wait for it to catch up, terminate the connection for waiting too long. Now you have to start the entire video over from the beginning.
Web video comes from two major sources: Those that provide their own content (such as those run by TV Networks), and those that provide content uploaded by users. The latter almost all have good players, since unlike the TV networks they can't afford not to. The biggest of these is YouTube, launched in 2005, and similar sites including Vimeo and Dailymotion have sprung up since. But they don't allow porn. For that, there various are pay and free sites dedicated to that purpose. But you get what you pay for.
An emerging technology is HTML 5's <video> tag, which allows video files to be played directly without the use of Flash Player or other third-party plugins. The browser itself handles caching, and the controls can be customized to some extent, the same way one customizes the look of the page itself. So far, only certain browsers support this tag, and there is a bit of a format war going on not unlike the one that once raged between VHS and Betamax: Mozilla Firefox has pledged to only support the open-source but rarely-used OGG Theora format, while Apple's Safari only supports the very popular but technically proprietary h.264. Microsoft's Internet Explorer 9 uses h.264 also; although Internet Explorer 6, 7, and 8 support neither. So it will be a while before Flash-based players go away entirely, as much as Steve Jobs (or Tim Cook) may wish/have wished otherwise.