I haven't put a lot of thought or research into offensive spells through my familiar yet as I haven't gotten that far. I was looking forward to using her for touch healing spells from across the battlefield since my party doesn't have a healer beyond my bardlock.
You get, at 15th level, access to one of the most powerful invocations - at will hold monster vs some of the most common and deadly monsters frequently found at those levels. That's something.
Of course, a familiar like an Imp, who can fly and be invisible while using the Help action, can grant you Advantage every turn with little risk of being killed (since they're not attacking, and it would cost an action to retaliate even if the foe knew where they were). That's something a normal familiar can't really do without high risk of death.
I’ve used the combo of casting bestow curse through my familiar in my game (using Sign of Ill Omen). It’s a bit combative but I can understand not wanting to take it since it uses a slot and only refreshes on a long rest. On the other hand, when it’s cast with a 5th level spell slot it no longer requires concentration.
I did a count of all "Touch" spells in the Warlock's list and I got a total of 11, not a single offensive one.
I currently have a Pact of the Tome using the Wizard's Familiar and have been considering using my Familiar to deliver Shocking Grasp, but as Mistwell pointed out the Help Action with Advantage is great. Sadly it's a little less awesome for the Warlock because it's to one roll and Eldritch Blast as it levels is multiple rays. So the familiar can only buff one of them.
My problem with using the Warlock's familiar is that attacking drops Invisibility, which makes them open to attack. Remember an Invisible Familiar doesn't draw Attacks of Opportunity because you can't give AoOs to targets you can't see. So an invisible familiar can run/fly around the battlefield lending aid and have the benefits of "Flyby" unless the target can see invisible. On the other hand the Warlock's familiar is the best kind of Scout. It's invisible, you can see through it's eyes up to 100 feet. We've used this to our advantage many times because the party then has full tactical awareness of the next room before we arrive. If your party is all in light armor and trained in stealth you're almost certain to have a surprise round! Plus the familiar has opposable thumbs, so that's never anything to sneeze at. We had the invisible familiar pickpock the Big Bad before a fight.
That said even if you had a good Touch spell, the Familiar acts on it's own Init, so you use cast the spell, and the Familiar uses it with a ReAction on it's own turn... I don't think the mechanics were well thought out. It's like mounted combat... the mechanics just doesn't feel right.
The more I think about good combos for the Warlock the more I realize that quite a lot are impossible due to available spells and or Feat design.One thing is the Warlock lacking the Dragon's Breath spell.
What sounds like a fun combo is aforementioned spell and - for example - an imp familiar. As the breath is an action but by definition not an attack, the imp should stay invisible while it keeps exhaling. But a character had to be Warlock 3, Sorcerer 3 or something like that...
Plane Shift can be used offensively, to perma-ban a hostile creature to another plane. It has a range of touch. Is your Warlock 13th level yet? LOL
Bestow Curse is available through the Sign of Ill Omen Invocation at 5th level. I've always hated these types of Invocations: if I need to burn an invocation slot, a spell slot, and a long rest to cast one freaking spell, well... maybe I just don't need that freaking spell, and if 5E's designers didn't want me casting it they just should have said so instead of pulling this "Yes, you can cast this spell by blowing a completely unreasonable pile of resources and gimping your freaking character" nonsense. [/tirade mode off] Ahem... I hadn't thought about sending forth an invisible familiar armed with Bestow Curse; that's almost worth doing.
How great would it be if Inflict Wounds and/or Dragons Breath were in the Warlock spell list? These are great offensive options for a familiar. I guess 3 levels in Divine Soul Sorcerer could get you both spells...at the cost of 3 levels of warlock. Not sure if the dip is worth it.