Here are the main alternatives to AdMob divided into tiers based on scale:
Tier one:
a) MoPub
b) Amazon Publisher Services
c) Facebook Audience Network
Tier two:
a) Verizon
b) Smaato
c) Fyber
d) MobFox
e) InMobi
f) AdColony
g) Rubicon
h) AppNexus
i) Pubmatic
j) OpenX
k) Chartboost
l) Unity Ads
m) Vdopia
n) IronSource
o) Adtoapp
p) AdinCube
q) Appodeal
r) PubNative

Let me explain them one-by-one:
1. MoPub: MoPub is another industry leading SSP option. It was an early entrant in the space, and it was acquired several years ago by Twitter. Since then it has continued to develop and it runs one of the largest exchanges for mobile app inventory, tapping into the advertiser base of Twitter.
2. Amazon Publisher Services (APS): Amazon Publisher Services is one of the newest options available to mobile app developers. Amazon has been rapidly developing their advertising capabilities and they have their own massive demand source because of all the merchants advertising on their platform. They also run a product called Transparent Ad Marketplace (TAM) that allows you to mediate other demand sources as well. It's not as easy to use as AdMob, but it's a very potent competitive option.
3. Facebook Audience Network (FAN): Facebook is the only other demand source that truly rivals Google AdMob in sheer size. FAN is not a mediation service, but it is so large that many apps would not need anything else, so it is an AdMob alternative. It is possible to use it as a demand source in other mediation solutions and if you can, you should.
4. Verizon (aka Nexage and Oath): The name of this one keeps changing. It was originally known as Nexage, which was another older exchange and SSP. Nexage was acquired by Millennial Media, which was acquired AOL and marketed as a product called One Mobile, then AOL was acquired by Verizon. Verizon deals in all digital ads, whether desktop, mobile web or mobile app. They have a full-featured SSP option and they are also providing header bidding to publishers.
5. Smaato: Smaato has traditionally been more internationally focused but has started to perform well in the US too. They have a sizable exchange of their own.
6. Fyber: Fyber is a roll-up of a few different companies, one of which was Inneractive which has a good-sized ad exchange for mobile app traffic. Fyber is a game focused SSP but they can and do operate on a variety of other types of apps. The mediation platform HeyZap was also acquired and rolled into Fyber.
7. MobFox: MobFox is the in-app monetization arm of the Matomy group.
8. InMobi: InMobi has long been a large ad network in international markets and a while back they acquired Aerserv. Aerserv is a video focused SSP with a mediation platform and exchange that performs well in the US, making it a great addition to InMobi.
9. AdColony: Many of these SSPs were formed through acquisition, and AdColony (formerly known as Opera) is a successful public company that was created through several acquisitions. Their SSP offering is underpinned by a mobile ad serving and mediation layer called AdMarvel. That platform is augmented by demand from a performance network formerly known as Moolah Media and a brand network formerly known as Mobile Theory. All of this has been combined and they have created their own proprietary exchange as well under the brand AdColony
10. Rubicon: Rubicon is a long-time player on web inventory. They grew rapidly and ultimately went public a few years ago. Rubicon operates a large exchange, and they have an SSP offering for in-app inventory, but their roots are in web inventory.
11. AppNexus: AppNexus runs a large exchange that traditionally was focused on web inventory. Again, their roots are web, but they are moving aggressively into app inventory as well. AppNexus is a more robust platform than other SSPs, which is a pro and a con. It can be used as a platform to run a whole ad network. However, that large scope of features can make it daunting to use as an SSP. As part of that platform, it has a very robust direct ad serving offering.
12. PubMatic: PubMatic is a large company running their own exchange. PubMatic acquired mobile ad network Mojiva a while back and Mojiva's ad serving counterpart Mocean, so they do have a robust direct ad serving system that can be used to operate a whole network, like AppNexus. That acquisition also gave them some technology that was developed specifically for mobile.
13. OpenX: Yet another large SSP from a private company with web roots. OpenX operates an exchange that is large and worth accessing. OpenX started as a direct ad serving platform and that is still one of their core offerings. They are one of the few SSPs that has a robust direct ad serving option.
14. Chartboost: Chartboost focuses exclusively on game apps. They run interstitial and video ad formats only and offer cross promo and a direct deal marketplace so you can coordinate with other app developers.
15. Unity Ads: The Unity platform for game development has an ad platform called Unity Ads woven into it. This makes it extremely easy for apps developed on Unity to use, but it focuses on rewarded video units exclusively.
16. Vdopia: Vdopia runs an optimization platform and video ad exchange called Chocolate.
17. IronSource: IronSource is a full-featured platform with a variety of ad units available, but they tend to focus on game apps and on rewarded video. If most of your inventory is rewarded, do NOT skip over this one. It is one of the leaders in that space.
18. Adtoapp: 20+ demand sources and monthly pay-outs.
19. Appodeal: 60+ demand sources and flexible payout options.
20. AdinCube: Ogury acquired this product and turned it into their publisher solution.
21. PubNative: Native ad network and good mediation add-on for other SSPs.

Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath

InMobi is the best alternative to admob for mobile display advertising . The reach is truly global alternatively you can use millennial media

InMobi is good, but we had 2x more volumes with MisterBell on a particular launch last year.

From my point of view you should usually stay away from comments that just state "the best is xxx". there dis no best, it all depends on your niche/target, user flow/experience and desired formats. There are a ton of ad networks, not to mention ad mediation and RTB to choose from.