Allies are something that an Angmar army must carefully select, as often they are the key to tying together a force. Angmar's own list lacks some very notable elements: characters that are not monsters (other than the ringwraiths), artillery, cavalry that is not undead, and monsters that are not characters. Thus, to get any of these things into the list, you have to take them as allies.
From my experience playing, the majority of units are not suitable allies to an Angmar force. Either they don't do anything you don't already do (such as taking Morannon Orcs when you could take Carn Dum Barbarians and not use up your ally points), or they do things that are useful for some armies, but not for yours (such as Uruk-hai crossbowmen or Corsair Arbalesters in a spirit army, as they are likely going to be great for the first turn or two, then be left behind and isolated, thus dying horribly).
This list is intended to provide some suggestions for allies that bring more than just their inherent value as a unit to the table, but rather synergy with the entire Angmar list (ignoring thematic concerns for now):
Morgul Stalker Warband - the key elements here are the ambusher and prowler abilities that these guys have. In a fast moving spirit list, they can spring out and often sucker punch people in the side or the rear, as the main focus of the opponent is going to have to be your spirits. If you use them to create another threat vector in a maneuver-based army, they can have significant value. To a lesser extent, the Orc Tracker Warband can do a similar job, but they are ultimately limited to a shooting role unless you want them to get chewed up in combat.
Black Guard of Barad Dur - in the barbarian heavy list, this can be the unit at the center of your army that the opponent absolutely must deal with, no exceptions, and no real way around it. They are a wrecking ball, and when you can surround them with other units that suck to be charged by, often your opponent will be faced with the unpleasant choice of which angry, berserk mob he would like to be punched repeatedly in the face by.
Siege Bow Battery - of all the artillery options, this one seems to fit Angmar the best. The catapults and Isengard ballista are significantly more expensive, so harder to fit into a limited allies allowance (though if you have the points, consider them as well). The 48" range means you can deploy them significantly out of the way and often get several turns of shooting out of them before they are annihilated by your opponent if the rest of your army has left them behind (though in the traditional barbarian army, they often can survive while your opponent has more pressing issues to deal with). Similarly, they can be used as the bait for a trap, forcing your opponent to deal with them or absorb their firepower every turn, and you can pop Buhrdur out of nearby terrain when a unit comes to deal with them, leading to their demise and the continued effectiveness of your artillery.
Feral Uruk-hai Warband - see my comments about the Morgul Stalkers. They are a very similar unit, with a bit more power on the attack and more courage at the cost of 5 more points per company and the prowlers ability. In reality, either one of these two units could serve the purpose you need them to effectively. I would be tempted to squeeze these guys in if I have the points to do so, but that can be a big if.
Wild Men of Dunland - the super-cheap version of ambushers. The least reliable, but the most numerous and easiest to wedge into an ally spot. One more trick to have up your sleeve as an Angmar player, especially if you are short on points but need more bodies on the field.
Thrydan Wolfsbane - cheap as hell, epic strike, resilience 3, and inspiring leader for your barbarians. Thrydan is an excellent ally choice to lead your barbarian hordes, especially if you want a less vulnerable character than a chieftain in one of the formations, and don't have a spare ringwraith.
Grima Wormtongue - minus two courage for a key enemy formation. You have dudes with spirit grasp and terror. Need I say more?
Moria Goblin Warband (and all goblin variants) - cheap bodies with master pathfinder and movement 8. One of the only ablative armor formations that can keep up with spirits, so if you are playing a spirit heavy army and need bodies, this should be a consideration. Keep in mind they will absolutely need a character to be able to at the double, but this is often a very good way to hide the Tainted in a reasonably sized unit that can keep up with your spirits. Perhaps one of the best allies for the spirit-heavy army, oddly enough.
Cave Troll - for the barbarian army, the cheapest non-character monster you can get your hands on. He makes a good enhancing unit to cover the flanks of barbarian units, and can help you win combats by piling in the front or the side when necessary. Also immune to ES duels by virtue of not being a hero, which can be oddly useful for a support unit.
Druzhag - normally, wilderness magic and ruin magic are both off limits for an Angmar army. Despite that, there are some very beneficial spells in both schools (especially ruin, where direct damage, dark fury, and sunder shields all have significant synergy with some of the direct bashing units like barbarians), and the ability to summon units that serve as ablative armor for your spirits is also a handy thing. I am typically leery of non-epic strike heroes, as they can lose combats for you at very inopportune times, but I'd suggest parking him either with a barbarian unit he can fall back out of, or an orc unit that is simply not important to limit the damage this can do to you.
Watchers of Karna Warband - once again, see my comments on ambushing formations above. Notably, I like these guys less than most of the others, as poisoned weapons is less valuable than berserk, roughly the same value as prowlers, and worse at times than the charging ability of the wild men. Just not compelling for the points in this particular context.
Black Numenorean Regiment - heavy infantry that causes terror. Here, if you are taking other units that reduce courage and intend to be playing games with terror, these guys can bring some value to the list. I don't think they are all stars, however, and the barbarians are likely better without being allies, so I would mostly leave them out. However...
Morgul Knights - these are the best heavy cavalry you can ally. Your ghostly riders have neither their defense nor lances, they also cause terror, they can be lead by a relatively mean character, and they are significantly cheaper than spirits. Basically, if you are going to ally in cavalry, you should be allying in these guys. They are great on their own, fill a hole in your list that you don't have a way to fill similar to the siege bows, and have terror to benefit from any courage issues you are creating. A strong consideration for the barbarian style list, and if you are using a spirit list, these guys can still keep up (barring terrain) with a solid character leading them.
Dalamyr, Fleetmaster of Umbar - one of the problems that you will face is your barbarians fare poorly being charged, and sometimes devastating cavalry charges are the bane of your army. There are no pikes in the Angmar list, and Dalamyr is often your best solution to this kind of issue. He's relatively cheap, has resilience 3 with epic strike to avoid death by duel, and denies the enemy a charge bonus when hitting his formation. Dalamyr in a large unit of barbarians will prevent cavalry from blowing them up, as their base attacks are often not nearly enough to win a fight, and if you have a turn where something absolutely must die, you can use an ES duel or Epic Poison with berserk (and possibly SfC'ed) barbarians to annihilate an enemy unit at a key juncture.
As a side note, Suladan and Amdur both provide inspiring leader for the Barbarians, and are brutal duelists themselves, but neither solve the cavalry problem nor are they cheap enough that you can take them as allies in smaller games, so consider them to have an honorable mention as allies.