To predict 10 years into the future is a very long time in technology but perhaps a look back will help.
Let's zoom back to 2002. At the time there were only GSM and GPRS networks deployed in Europe. Mobile was was already ubiquitous but mobile data was just at the very beginning with a data rate of just a few kilobits per second over the air. UMTS was already standardized in Release 99, with efforts having started in the mid 1990's, but networks were not available yet. UMTS HSDPA was standardized in the 2002 timeframe when networks were not even launched and the uplink part HSUPA followed in 2004. In other words, the wireless technologies we are using today were first thought of about 12 years ago and then put into standards which were finalized around 10 years ago. Wikipedia has a good overview of which 3GPP Release was published when. LTE networks have launched in the meantime as well and their standardization started in 2004, even before I had my first UMTS phone, as described in further detail here.
With that in mind, let's have a look what's currently being standardized by 3GPP. Unlike 10 years ago, no move to a new revolutionary air interface technology is on the agenda like the move from GSM to UMTS previously. So the acronym LTE (Long Term Evolution) holds true to its name so far. The reason for that is that with LTE all angles of increasing data transfer rates are being explored. Ever higher modulation and coding schemes, MIMO, sectorization, beamforming and carrier aggregation across diffrent bands are possible from a standardization point of view and only the hardware implementation and physical nature of the radio channel are the limit. This is different to GSM with its focus on 200 kHz (0.2 MHz) channels and its voice centric timeslot design. Also, UMTS came to its limits in the frequency domain with its 5 MHz channels. The standard evolved over time to allow carrier aggregation and many networks and some device implement the dual-carrier variant by now. But several carriers was not in the mind of engineers from the beginning so aggregating more becomes cumbersome from a protocol point of view. As everyone is going to LTE anyway I doubt we'll see more than two carriers aggregated in the future.
So without any other air interface technology currently in the specification phase it's pretty certain that the networks we'll have in 10 years from now will still be based on LTE. LTE macro networks are still being expanded, however, so the LTE networks 10 years down the road will be much more ubiquitous than today and also much more dense in metro areas to satisfy the increasing demand. While in the US most networks use a 10 MHz LTE carrier today and 20 MHz carriers are used by many networks in Europe, most network operators have bought much more spectrum and will start using it once more capacity is needed. Whether channels will mostly be used independently and users are scheduled on different channels and bands depending on the channel load and local transmission conditions or whether mobiles will be able to aggregate channels beyond 20 MHz is, from my point of view, not quite clear. The standards exist to aggregate several 20 MHz channels but if this will happen in practice is another matter. But hardware evolves and when looking back 10 years and what radio interfaces of mobile devices were capable then (remember, there wasn't even UMTS at the time in practice) I guess one should never say never.
Except for using ever more spectrum, other angles of approach to increase the capacity of the network without increasing the highest data rate achievable by mobile devices is to use techniques such as using 6 instead of only 3 independent sectors per base station and to bring beamforming technologies to fruition that concentrates the available power during the transmission of data to a particular user into his direction.
What I think that we won't see is a further densification of the macro layer beyond what we have with 2G and 3G today. As described here, the range of one sector in a cell is typically already 300m or less today in densely populated areas. To get to a cell range of 50m or less such as in some parts of Seoul, new approaches are required. Small cells is the buzzword when further densification is required. Small refers to the size of the base station and the antenna which should be integrated and not much bigger than today's Wi-Fi access points so they can be deployed anywhere quickly and cheaply. Small also referrs to the power output and thus the range and area covered by that radio. The smaller the cell the higher the overall capacity of the network as the channel can be more often reused.
Apart from getting a backhaul link to small cells, another challenge is how to mitigate interference at the many cell edges as interference has a significant impact on data transfer rates at those cell borders. The straight forward approach is to have them work independently from each other and let them coordinate in the same loose fashion as today in the macro network by handing over ongoing connections and manage inter-cell interference by cooperation between the cells. Another, albeit more complicated approach, is Heterogeneous Networks (HetNets, eICIC) and Coordinated Multipoint (CoMP) in which the smaller cells are tightly coupled with a macro cell or are even remote radio heads controlled by a central scheduler. Which of these approaches will be dominant in 10 years from now is difficult to tell. Perhaps simplicity trumps over complexity. On the other hand, 10 years is a long time to perfect HetNet and CoMP.
Needless to say is that Wi-Fi will also be around in 10 years from now and will play an ever more important role at home and work. New standards such as the 802.11ac extension will further increase data rates in such places, which will certainly be needed as DSL, cable and fiber backhaul to homes are already today often exceeding the practical transfer speeds achievable with 802.11n through typical home environments with several rooms and walls between access point and devices. In theory, public Wi-Fi hotspots could also be more tightly integrated into cellular networks to offer higher localized transmission speeds. Standards exist for such a coupling but I am skeptical that they will really be implemented. On the one hand, Wi-Fi is a completely unmanaged component in mobile devices today and users have full control over it. Changing this might not be very desirable from a mobile device manufacturer, operating system and user point of view. Also, there are other alternatives such has HetNets and CoMP on the other hand that can be implemented mostly on the network side and as part of the baseband radio chip in mobile devices.
And finally, there's the voice gap in LTE networks today. Currently, all major networks still use either a dual radio approach (e.g. Verizon) or fallback to GSM or UMTS. Migrating to an operator based Voice over LTE service requires a lot to be put in place. First, network coverage must become much more ubiquitous than LTE and even 3G networks are today. While I can have an ongoing voice call on my daily train commute without any call drops, there are several data outages on the 3G layer that that would kill any Voice over LTE call. But since we won't get there anytime soon, a fallback to traditional GSM or UMTS circuit switched channels for IP voice calls needs to be put in place. This is called Single-Radio Voice Call Continuity (SR-VCC) and more details can be found here. The feature behind SR-VCC is IMS Centralized Services and the practical implementation of this in real networks is likely going to be a major pain. But I can imagine that in 10 years from now LTE networks are ubiquitous enough for true voice over LTE without many fallbacks required anymore. It won't come cheap, however, to get the same voice call quality and very low drop rates we have today in many networks.
In short, there are currently no plans to replace LTE with anything different in 10 years from now, unlike previously where UMTS was not even out of the tracks when a successor technology was already in the making. Instead, the LTE air interface will be refined as networks become denser and capacity requirements increase.