Charging Li-ion batteries in parallel
The essential bit [not explicitly mentioned in the other answers] is [by all accounts] matching the internal resistances of the cells. Which according to sellers can only be done reliably at factory.
The MIT boffins have studied this too and quantified the impact of mismatched resistance:
a 20% difference in cell internal resistance between two cells cycled in parallel can lead to approximately 40% reduction in cycle life when compared to two cells parallel-connected with very similar internal resistance
And since you'll probably be interested in measuring this internal resistance yourself, this is how they've done it for 2.2 Ah batteries:
Internal resistance was measured at 50% state of charge (SOC) with a 15 s DC pulse of 40 A (17C). While there is no commonly accepted standard for measuring the internal resistance of lithium-ion batteries, we chose this current and time profile because it is relevant to the duty cycle seen by these cells in hybrid vehicles and power tools. A comparison of several methods for the internal resistance of lithium-ion cells is provided by Schweiger et al. [3]. The 15 s current pulse allows the effects of the mass-transfer limited reaction to show. Longer delay times can lead to significant self-heating of the cell which affects the measured internal resistance. This 17C discharge rate is within the specified rating for this high-power cell, of 32C continuous discharge and 55C for 10-s peaks. The characterization tests were done on bare cells in a background room temperature of 25 C. The resistance difference between the most and least resistive cells was 24.7%. The maximum difference in capacity in this same batch of cells (one full discharge cycle at 17C continuous discharge current) was 3.6%. For the purposes of this experiment, the differences in initial capacity were considered to be negligible compared to the differences in internal resistance.
[3] H.-G. Schweiger, O. Obeidi, O. Komesker, A. Raschke, M. Schiemann, C. Zehner, M. Gehnen, M. Keller, P. Birke, Sensors 10 (6) (2010) 5604e5625, http://dx.doi.org/10.3390/s100605604
Connecting cells in parallel is common practise with professional battery pack manufacturers, so there is nothing wrong with it. What pros do is they assemble packs from cells out of the same box (same shipment, same lot), having very tight tolerances. This way, you even get packs with serially connected cells (eg. 3s1p) where the cell voltages stay closely matched over the lifetime of the pack (several years) - without balancing of course. This is quite a considerable achievement, you can calculate yourself how much self discharge difference the cells can have in order not to have significant unbalancing.
Your case is much simpler (1s2p) so I guess you are using low quality cells. The above is only valid for top quality cells (Panasonic, Samsung etc), a lot of "noname" cells like used in aftermarket camera batteries are just crap. Which cells are you using?
Li-Ion cells in parallel work very well as long as they are in exactly the same condition. If one cell is degraded, it will cause the other(s) to slowly discharge in order to compensate for the lower voltage the degraded one will have. Your pack will inevitable have lower capacity and will present problems when charging (bad cell may overheat so much that it even starts a fire while the other(s) will be unable to reach 100% charge).
As a good practice, charge individual cells to full, then discharge them to around 80% (use same load and same time interval for each) and then let them stabilize for a while (few hours is very safe, but minimum 15 minutes will do). Then measure the voltage of them all and make a pack out of the ones that have the nearest voltage compared to each other. For example, if you have 5 cells and you need to make a 3-pack and they show 3,8, 3.92, 3.93, 3.95, 4.01, exclude the 3.8 and 4.01 ones from the pack. It means the first is in bad shape, the last is in excellent shape and the other 3 are good enough to be used.