No, sorry, not the Star Trek novel by Diane Duane (one of her Rihansu series). (One of the few Trek novels I actually enjoyed, btw.)
Enemy is one of those disadvantages every one of my players seems to want to take, mostly because they know I'll either end up working the enemy into the game, or ignoring it completely, hence giving them free points. (This latter point is especially true when I have a party Enemy already planned; personal Enemies tend to be side plots and sub-plots, and harder to work in.)
One of the key items with Enemy is scope. In my games, I make it a point that you cannot have an entire national government as an Enemy, particularly just for existing. Even if most of that government has an Intolerance to your race/species/occupation - such as many in the the Rifts Coalition States effectively having Intolerance (Mages), Intolerance (Non-Humans), or Intolerance (Total) - taking Enemy (Government) means that the entire government is actively hunting you down, putting your name and face at the top of the Public Enemies List. Even taking a government agency as an Enemy is not normally allowed in my games; the exception being Law Enforcement for criminals with warrants for their arrest.
For players that want to take an entire government or government agency as an Enemy, I commonly ask them, "Who did you piss off?" Sometimes, I get "well, I'm a mage/unlicensed psi/illegal alien/whatever. so shouldn't I have them as an Enemy?" Then I carefully explain other possible disads that would be a better fit (Social Stigma comes into play quite often here). Sometimes I get, "Lieutenant-Detective Columbo, LAPD" (or some other low ranking officer in an limited agency). That's when I strongly suggest making that person an Enemy rather than the whole department. (If that person can be construed as having some form of Rank, such as Columbo's Police Rank 1, then I help the player price the Enemy accordingly.)
Enemy also comes in three levels: Watcher, Rival, and Hunter.
Watcher means that the Enemy is not out to harm or even humiliate you; he's simply keeping tabs on you for some reason. This can be inconvenient, but rarely harmful. Think of the Watchers from the Highlander television series; they're keeping tabs on the Immortals, and sometimes end up being casualties in the quest for the Prize; they're an Enemy of the Immortal they're following in the sense that the organization they work for does not necessarily have the Immortals' interests at heart. (In keeping with the title of this post, they can also be Allies....) Such an Enemy may be Unknown to the PC without it affecting the long-term campaign that much; in this case, the GM may just decide to have the PC's exploits get in the news once too often.
Rival is someone you've pissed off enough that they've decided to make your life uncomfortable, or just that your interests run perpendicular to theirs that they decided to be a pain. A notable case for this may be the various depictions of Turk Barrett in the Daredevil comics, movie, and series; quite often, Turk would have Enemy (Rival: Daredevil), or so it would seem at times from Turk's point of view (Daredevil doesn't intend harm toward Turk specifically, but he always seems to stumble upon some scheme of Turk's and wreck it, even without Turk going to prison after). In one game, I had a character take a Rival Enemy in his own department; his boss hated him and was making his life miserable.
Hunter means that the Enemy wants to eliminate you; this doesn't necessarily mean they want to kill you; they may maim you, render you permanently unconscious, imprison you, force you into permanent exile, or something similar that basically removes you from the world.
So, now that one of my PCs has an Enemy, how do I work him into play?
This depends greatly on the game at hand. A Watcher and Rival is easily worked in as a recurring NPC in most games, regardless of genre. A Hunter is harder to work in, and I would ask that the player take a lower Frequency of Appearance on such an Enemy to prevent the Enemy from derailing the campaign to one solely about that Enemy. An every so often Enemy is sometimes more fun than a full-time one, as the players may get tired of fighting the same guy(s) over and over.
I want my players to have a campaign Enemy. Should I charge points for this?
For a Watcher or Rival, I'd say "Yes". For a Hunter, this looks like it'll be a major overall plot point for the campaign. In this case, I would say "No".
Allow me to explain my reasoning. A Watcher or Rival adds flavor, and may be useful even if working at cross-purposes to the party. A Hunter as a Party Enemy is probably the point of the campaign, and therefore essentially a campaign feature.
I should note that much of this advice is also suitable for the Ally advantage.
As with all options, err on the side of having fun. Some parties will enjoy having an Enemy Hunter that shows up every session, while others will rather have the Enemy Watcher show up taking photos of Things Man Is Not Meant to Know or an Enemy Rival messing with the paperwork rather than a Hunter trying to kill them for the thirtieth session in a row. My own advice is to arrange things in moderation and with variety, not monotony.